Here is an example of how to send a file with SFTP:

<?php

class SFTPConnection
{
    private $connection;
    private $sftp;

    public function __construct($host, $port=22)
    {
        $this->connection = @ssh2_connect($host, $port);
        if (! $this->connection)
            throw new Exception("Could not connect to $host on port $port.");
    }

    public function login($username, $password)
    {
        if (! @ssh2_auth_password($this->connection, $username, $password))
            throw new Exception("Could not authenticate with username $username " .
                                "and password $password.");

        $this->sftp = @ssh2_sftp($this->connection);
        if (! $this->sftp)
            throw new Exception("Could not initialize SFTP subsystem.");
    }

    public function uploadFile($local_file, $remote_file)
    {
        $sftp = $this->sftp;
        $stream = @fopen("ssh2.sftp://$sftp$remote_file", 'w');

        if (! $stream)
            throw new Exception("Could not open file: $remote_file");

        $data_to_send = @file_get_contents($local_file);
        if ($data_to_send === false)
            throw new Exception("Could not open local file: $local_file.");

        if (@fwrite($stream, $data_to_send) === false)
            throw new Exception("Could not send data from file: $local_file.");

        @fclose($stream);
    }
}

try
{
    $sftp = new SFTPConnection("localhost", 22);
    $sftp->login("username", "password");
    $sftp->uploadFile("/tmp/to_be_sent", "/tmp/to_be_received");
}
catch (Exception $e)
{
    echo $e->getMessage() . "\n";
}

?>

Note that you must enter the full wrapper URI order for functions that accept those parameters to work properly. For example, this (which is referenced more than once in other comments) does not work:

while (false !== ($file = readdir($handle))) if (is_dir($file)) { /* ... */ }

This does work:

$sc = ssh2_sftp(...);
while (false !== ($file = readdir($handle))) if (is_dir("ssh2.sftp://$sc/$file")) { /* ... */ }

You need to pass the "path" into these functions as an fopen() wrapper URI.

I added some functionality for scanning the filesystem and receiving and deleting files.

class SFTPConnection
{
    private $connection;
    private $sftp;

    public function __construct($host, $port=22)
    {
        $this->connection = @ssh2_connect($host, $port);
        if (! $this->connection)
            throw new Exception("Could not connect to $host on port $port.");
    }

    public function login($username, $password)
    {
        if (! @ssh2_auth_password($this->connection, $username, $password))
            throw new Exception("Could not authenticate with username $username " . "and password $password.");
        $this->sftp = @ssh2_sftp($this->connection);
        if (! $this->sftp)
            throw new Exception("Could not initialize SFTP subsystem.");
    }

    public function uploadFile($local_file, $remote_file)
    {
        $sftp = $this->sftp;
        $stream = @fopen("ssh2.sftp://$sftp$remote_file", 'w');
        if (! $stream)
            throw new Exception("Could not open file: $remote_file");
        $data_to_send = @file_get_contents($local_file);
        if ($data_to_send === false)
            throw new Exception("Could not open local file: $local_file.");
        if (@fwrite($stream, $data_to_send) === false)
            throw new Exception("Could not send data from file: $local_file.");
        @fclose($stream);
    }
    
        function scanFilesystem($remote_file) {
              $sftp = $this->sftp;
            $dir = "ssh2.sftp://$sftp$remote_file";  
              $tempArray = array();
            $handle = opendir($dir);
          // List all the files
            while (false !== ($file = readdir($handle))) {
            if (substr("$file", 0, 1) != "."){
              if(is_dir($file)){
//                $tempArray[$file] = $this->scanFilesystem("$dir/$file");
               } else {
                 $tempArray[]=$file;
               }
             }
            }
           closedir($handle);
          return $tempArray;
        }    

    public function receiveFile($remote_file, $local_file)
    {
        $sftp = $this->sftp;
        $stream = @fopen("ssh2.sftp://$sftp$remote_file", 'r');
        if (! $stream)
            throw new Exception("Could not open file: $remote_file");
        $contents = fread($stream, filesize("ssh2.sftp://$sftp$remote_file"));            
        file_put_contents ($local_file, $contents);
        @fclose($stream);
    }
        
    public function deleteFile($remote_file){
      $sftp = $this->sftp;
      unlink("ssh2.sftp://$sftp$remote_file");
    }
}

I changed the read function to:

    public function receiveFile($remote_file, $local_file)
    {
        $sftp = $this->sftp;
        $stream = @fopen("ssh2.sftp://$sftp$remote_file", 'r');
        if (! $stream)
            throw new Exception("Could not open file: $remote_file");
        $size = $this->getFileSize($remote_file);            
        $contents = '';
        $read = 0;
        $len = $size;
        while ($read < $len && ($buf = fread($stream, $len - $read))) {
          $read += strlen($buf);
          $contents .= $buf;
        }        
        file_put_contents ($local_file, $contents);
        @fclose($stream);
    }

    public function getFileSize($file){
      $sftp = $this->sftp;
        return filesize("ssh2.sftp://$sftp$file");
    }

The sftp class provided by David Barnes works great.  However, if you get errors about fopen and it failing to open a stream, try the fully qualified path on the remote server.

For example, if you are uploading a file to /Users/username/Sites/file.txt this may not work:

<?php
try {
    $sftp = new SFTPConnection("localhost", 22);
    $sftp->login("username", "password");
    $sftp->uploadFile("/tmp/to_be_sent", "Sites/file.txt");
}
catch (Exception $e) {
    echo $e->getMessage() . "\n";
}
?>

but this will:

<?php
try {
    $sftp = new SFTPConnection("localhost", 22);
    $sftp->login("username", "password");
    $sftp->uploadFile("/tmp/to_be_sent", "/Users/username/Sites/file.txt");
}
catch (Exception $e) {
    echo $e->getMessage() . "\n";
}
?>

Don't assume that since you are connecting as that user that you are starting in its home space.

Another possible option is that you need to use http://us.php.net/manual/en/function.ssh2-sftp-mkdir.php first to make the directory if it does not exist already, and then upload the file into it.

When uploading (writing) a file you must use an absolute path, not a relative one. 

If, like me, you want to use a relative path, you can use the following code: 

$fh=fopen("ssh2.sftp://$sftp".ssh2_sftp_realpath($sftp,".")."/fileinmyhomedir.txt");

In

$stream = fopen("ssh2.sftp://$sftp/path/to/file", 'r');

please make sure that you are specifying the "absolute" path to a file.

If not, you'll get errors like

"Unable to open file ..."

The reasoning is simple ... ssh2.sftp://$sftp points to the "root" directory on the remote server, where, most likely, one does not have access.

It is necessary to point it to your "home" directory.  For example, "ssh2.sftp://$sftp/home/username/filename" ... where "/home/username" is where your home directory is.

If you wish to store once the protocol + ressource used ("ssh2.sftp://$sftp";)
There's a little trick to know... 
This won't work :

<?php
function connect(){
    $connection = ssh2_connect('shell.example.com', 22);
    ssh2_auth_password($connection, 'username', 'password');
    $sftp = ssh2_sftp($connection); 
    return "ssh2.sftp://$sftp";
}
$remote = connect();
is_file( $remote."/path/to/file"); 
// Warning
// Message: is_file(): ## is not a valid SSH2 SFTP resource
?>

You need to have $sftp still avaible at moment the function (is_file, filesize, fopen, ...) uses it
Otherwise, I guess the GC cleans it up and closes the ssh2_stfp connection
That's why this work :

<?php
function connect(){
    //...
    global $sftp;
    $sftp = ssh2_sftp($connection); 
    return "ssh2.sftp://$sftp";
}
$remote = connect();
is_file( $remote."/path/to/file");

// Or way better :

class myClass {
    public function connect(){
        //...
        $this->sftp     = ssh2_sftp($connection); 
        $this->remote   = "ssh2.sftp://".$this->sftp;
    }
    public function test(){
        is_file( $this->remote."/path/to/file");
    }
}
$obj = new myClass();
$obj->connect();
$obj->test();
?>

David's code works wonderfully except for one thing, it wouldn't upload a file until I placed a forward slash after '$sftp'
    
public function uploadFile($local_file, $remote_file)
    {
        $sftp = $this->sftp;
        // Original
        // "ssh2.sftp://$sftp$remote_file"
        $stream = @fopen("ssh2.sftp://$sftp/$remote_file", 'w');

        if (! $stream)
            throw new Exception("Could not open file: $remote_file");

        $data_to_send = @file_get_contents($local_file);
        if ($data_to_send === false)
            throw new Exception("Could not open local file: $local_file.");

        if (@fwrite($stream, $data_to_send) === false)
            throw new Exception("Could not send data from file: $local_file.");

        @fclose($stream);
    }

Adding a function to previous class to connect with key instead of user/password

<?php
public function loginWithKey($username, $publicKey, $privateKey, $passphrase = null)
  {
    if (!@ssh2_auth_pubkey_file($this->connection, $username, $publicKey, $privateKey, $passphrase)) {
      throw new Exception("Could not authenticate with given keys or passphrase");
    }

    $this->sftp = @ssh2_sftp($this->connection);
    if (!$this->sftp) {
      throw new Exception("Could not initialize SFTP subsystem.");
    }
  }

?>

Remember to use stream_set_chunk_size() on the resource for performance reasons, especially if you're uploading large files on links with high latency.

SFTP can only send 32K of data in one packet and libssh2 will wait for a response after each packet sent. So with a default chunk size of 8K the upload will be very slow.
If you set the chunk size to for example 1Mb, libssh2 will send that chunk in multiple packets of 32K and then wait for a response, making the upload much faster.
(see man libssh2_sftp_write for more details)

<?php
$connection = ssh2_connect('shell.example.com', 22);
ssh2_auth_password($connection, 'username', 'password');
$sftp = ssh2_sftp($connection);
$stream = fopen("ssh2.sftp://$sftp/path/to/file", 'w');

stream_set_chunk_size($stream, 1024*1024);
fwrite($stream, $data);
?>

Here is a modified SFTPConnection class previously posted that returns a recursive directory scanFilesystem method.

<?php
class SFTPConnection
{
    private $connection;
    private $sftp;

    public function __construct($host, $port=22)
    {
        $this->connection = @ssh2_connect($host, $port);
        if (! $this->connection)
            throw new Exception("Could not connect to $host on port $port.");
    }

    public function login($username, $password)
    {
        if (! @ssh2_auth_password($this->connection, $username, $password))
            throw new Exception("Could not authenticate with username $username " . "and password $password.");
        $this->sftp = @ssh2_sftp($this->connection);
        if (! $this->sftp)
            throw new Exception("Could not initialize SFTP subsystem.");
    }

    public function uploadFile($local_file, $remote_file)
    {
        $sftp = $this->sftp;
        $stream = @fopen("ssh2.sftp://$sftp$remote_file", 'w');
        if (! $stream)
            throw new Exception("Could not open file: $remote_file");
        $data_to_send = @file_get_contents($local_file);
        if ($data_to_send === false)
            throw new Exception("Could not open local file: $local_file.");
        if (@fwrite($stream, $data_to_send) === false)
            throw new Exception("Could not send data from file: $local_file.");
        @fclose($stream);
    }

    function scanFilesystem($remote_file) {
        $sftp = $this->sftp;
        $dir = "ssh2.sftp://$sftp$remote_file";
        $tempArray = array();

        if (is_dir($dir)) {
            if ($dh = opendir($dir)) {
                while (($file = readdir($dh)) !== false) {
                    $filetype = filetype($dir . $file);
                    if($filetype == "dir") {
                        $tmp = $this->scanFilesystem($remote_file . $file . "/");
                        foreach($tmp as $t) {
                            $tempArray[] = $file . "/" . $t;
                        }
                    } else {
                        $tempArray[] = $file;
                    }
                }
                closedir($dh);
            }
        }

        return $tempArray;
    }

    public function receiveFile($remote_file, $local_file)
    {
        $sftp = $this->sftp;
        $stream = @fopen("ssh2.sftp://$sftp$remote_file", 'r');
        if (! $stream)
            throw new Exception("Could not open file: $remote_file");
        $contents = fread($stream, filesize("ssh2.sftp://$sftp$remote_file"));
        file_put_contents ($local_file, $contents);
        @fclose($stream);
    }

    public function deleteFile($remote_file){
        $sftp = $this->sftp;
        unlink("ssh2.sftp://$sftp$remote_file");
    }
}
?>

if anyone is interested on how to get a directory listing:
$SSH_CONNECTION= ssh2_connect('shell.example.com', 22);
ssh2_auth_password($SSH_CONNECTION, 'username', 'password');
//------------------------------------------------------------------- 
//this function finds all files within  given directory and returns them
function scanFilesystem($dir) {
    $tempArray = array();
    $handle = opendir($dir);
  // List all the files
    while (false !== ($file = readdir($handle))) {
    if (substr("$file", 0, 1) != "."){
           if(is_dir($file)){
            $tempArray[$file]=scanFilesystem("$dir/$file");
        } else {
            $tempArray[]=$file;
        }
    }
    }
   closedir($handle); 
  return $tempArray;
}

//------------------------------------------------------------------- 
$sftp = ssh2_sftp($SSH_CONNECTION);

//code to get listing of all OUTGOING files
$dir = "ssh2.sftp://$sftp/outgoing";
$outgoing = scanFilesystem($dir);
sort($outgoing);
print_r($outgoing);