This will probably sound like a bit of a plug but whatever;
I use dropbox, you just stick the files into your Public folder1,3, right click the file and then click "copy public link", and that link is a direct web accessible link to the file on dropbox servers2.
1You need to make an account first.
2As soon as you put anything in your dropbox it gets uploaded to their servers.
3Everything in this folder is public, people say its a security issue, but isn't not like you don't have fair warning with a folder named "Public", your other folders are only available to the people assigned to them.