I can heavily suggest getting an acount on box.net - it's forever (at least it didn't delete my files from a few years back), doesn't change you with anything, keeps track of the number of downloads and all, and lets you sort your files in a designated file system. You can - which should be particularily interesting for project hosting - replace a file with another, keeping the URL the same and therefore allowing you to keep the URLs in different locations unchanged while just changing the file.
A downside might be that you can't upload larger than 25MB, which is generally enough with smart project management, however for some reason I've never seen anyone but me and a handful being able to do it for large projects... so, I guess you're left with the method of splitting your files in that case still. That isn't too awesome (even packing them in a single file isn't), however because of the following stuff, it's not that bothersome:
Box.net doesn't have a daily download limit, nor does it make random people wait 60 seconds or whatever, or not allow downloads for a certain period of time afterwards. I'm pretty sure that applies for the methods mentioned by Alan as well, but it's still mentionable, as all of the shady filehosters like Rapidshare or Hotfile do that kind of stuff... and therefore are a no-go anyways.
The other, probably better way would be to find someone that hosts your game on his webspace, which you can accomplish for free if you'Re lucky finding someone. Then of course, try to get as sure as possible that it won't go down in the next few days :p
