Apple - Is it possible to upload files to a website from Safari on iPhone?

As of iOS 6, Mobile Safari now supports file (image) uploads, from the Camera Roll, albums, and photostreams. Note that iOS 6 is only available for the iPhone 3GS and newer.

Specifically the browse button is disabled because there isn't a file browser (like Windows Explorer/Finder) on the iPhone. Most people don't notice that, because the iOS is designed around avoiding the need for a user interface to the iPhone's file system.

For simplicity's sake file management is turned into a programing problem instead of a user problem. For security's sake applications can't directly access the documents of other applications.

As Jawa mention, a lot of sites have iPhone applications to allow uploads.

No, uploading from mobile Safari is not possible. That's why about every other site that utilizes user uploads (e.g. Flickr, Facebook, Picasa) have either made their own upload app for the iPhone, or there are some apps that can handle many sites, such as Pixelpipe.