Free Web Hosting

Honestly, my advice if you're at all serious about the site is to get a domain, but these are a great place for not so serious sites like a personal page or even a place to learn the basics of html and web design.

I'm only listing a few of the ones out there, but these ones have all been around for ages so they're likely to be around for many more years to come.

Bravenet
50 mb of totally free storage space (this is not webspace for your website, but you can use it to store files) with custom directory structures, easy uploads and downloads and unlimited access 24/7. You can share your files with friends and family or keep them private! You can change the look of your counter anytime without losing visitor information and change the value of your counter at anytime.

Prohosting
You get 250 MB of disk space with 10 gigs of transfer and custom CGI/SSI. For business or personal use.
Upload: FTP
Banners: None.
CGI: Yes

50Megs
50 megs of free webspace, FrontPage support, pop & web based email.
Upload: FTP, browser.
Banner: Top banner or pop up.
Address: http://yourname.50megs.com
http://yourname.i8.com
http://yourname.5u.com

Free Webspace.net
While I used to try to keep a rather large listing of free website hosts I don't have as much time to spend on Webweaver's listings anymore as I'd like. However, freewebspace.net has way more reviews that you could ever need, is updated often and is just generally a great resource if you're looking for free hosting.