I've solved that this way (I didn't find a plugin),
Install the ExecPHP-Plugin, and the Role Manager Plugin, create a page for Registered Users.
Put this HTML code in there:
<form enctype="multipart/form-data" action="uploader.php" method="POST">
<input type="hidden" name="MAX_FILE_SIZE" value="100000" />
Datei auswählen: <input name="uploadedfile" type="file" />
<input type="submit" value="Upload" />
create a directory in your wordpress root directory called
create uploader.php within the wordpress dir containing:
$target_path = "uploader/";
$target_path = $target_path . basename( $_FILES['uploadedfile']['name']);
header("Location: http://somewhere.com/success.php"); // where you want to go after succeeded upload
header("Location: http://somewhere.com/error.php"); // where you want to go after failed upload
That's only an example for a very easy upload form, but I wouldn't recommend any uploads at all, because security reasons.