Firefox users now has a handy add-on called "Dragdropupload," that bypasses that annoying "browse" or "choose file" button and lets you drop files directly onto an upload field. With Dragdropupload installed, you can still click browse if you want to, but simply dragging your file to the button should do the trick.
Drop multiple files and fill all the entries. In some websites it allows to add new upload files: in Google Mail is possible to drop the files directly over the "Attach a file" link.
A Sidebar allows to drop files from a listing
It's now possible to drop text snippets and the extension generates a temporary text file. This's useful with Thunderbird allowing to drop text from an email as a new .eml file.