Do you know of any good solution to receive small and big files from the public? For videos and photos of ongoing protest?

Box.net

Email + TransferBigFiles.com might be your best bet.

If you have access to dedicated hosting you can set up an upload script pretty easily, but on shared hosting (most places are shared) there’s usually a file size limit somewhere between 2GB and 8GB.

Check out this page on the TransferBigFiles site, it describes essentially the service you’re looking for (especially the screenshot at the bottom), but I haven’t used this before so I’m not sure if it would operate exactly as you need.