What applications will allow me to freely host and share a variety of files or documents? What are the limitations?
All you need is Dropbox. You can easily share big files with your friends and there is also an option for public shares. One folder that whatever you're putting there has a public link to it, so you can share it.
The only limitation is the 2GB for free accounts, but you can go up to 10GB if you'll invite people with a special link. Both you and who ever is registering via this link are getting +250MB for free.
If you don't want to install anything you can use Google docs where you have 1024 MB of free storage. Files can be converted to Google docs. OCR is supported as well. You can set sharing settings (public, accessible to anyone with the link, accessible to people you specify) for each file or for a bunch of files in one folder.
Check this help page for the details.