As has been mentioned before, using your own server is a good choice if you can handle the bandwidth. If that's not possible, I've had great relability and service with Ge.tt
Quote from the FAQ:
Ge.tt is 100% web-based and works directly in your browser. No flash required. No applet needed. No installation before you're ready to go. Just go to your browser and start sharing.
The free account will delete files after 30 days, however if YOU sign-up for an account then the files last until you remove them. (or Ge.tt gets sued into oblivion) Users who get the ge.tt link won't need to sign-up to download.
In order to clean its file storage, Ge.tt is entitled to delete files which have not been accessed for a longer period of time. However, this deletion shall only take place after minimum 30 days have passed since the file was uploaded, and if the user does not have an account.
Users of the Ge.tt services shall have the option of registering free-of-charge. Through this registration, they can expand the features and functions of the Ge.tt services and view and manage all files, which have been uploaded using this account.