I found a really nice post on different file storage apps, which I have shamelessly stolen, but if you'd like to visit the original it's here. I've deleted sites that no longer exist, added some from the comments field as well, and added in a tad more detail.
lets you store, manage and stream your media remotely, anywhere at
anytime through an awesome desktop-like application right into your
browser. You can stream at your desired and provided quality with no
data loss and no overcharges.
Free File Hosting Made Simple - MediaFire. This is impressive: unlimited storage, up to 100MB per file, unlimited up/downloads/bandwidth, image galleries, no signup required, no software to install. For nothing. Free. Zip. Nada.
Wonderfile. Store any kind of content, and make it available for other people to see. Free and commercial versions. Freebie version allows maximum file sizes of 10 MB, storage of 1GB and bandwidth of 2GB.
Omnidrive :: Free Centralized Online Storage. Omnidrive allows you to aggregate not only all your desktop files, but all your files and data from different web applications as well. You can exchange files and data between applications using Omnidrive, and also easily share and publish files with just a single click. Omnidrive is multi-platform and is available on both Windows and Mac, and also provides a browser-based version that emulates a desktop file browser. With Omnidrive you can:
1. Access - access all your files and data from anywhere 2. Integrate - integrate files and data from other applications into Omnidrive 3. Share - share to another user or an email address with just one click 4. Publish - publish music, video or photos to the web and link to them from within forums, blogs or websites
Inv.io | Unlimited storage for everyone!. It's a fast and extremely reliable file storage. Share your files faster: get links while uploading. Add entire folders with their multiple selection tool. Create and share picture galeries, video players. Use their file manager to edit your links in minutes. Send up to 1 Gb (1'000 Mb) per link for free. They keep your files online as long as needed.