Wow last post was from 11/06/
2001, since it's back let's update it:
Picture Hosting:
http://www.flickr.com/ - It's simply the best, tons of people use it. Especially the nerds who try everything
http://www.imageshack.us/ - Use this if you need something done quickly, it does lack the gallery feature
http://photobucket.com/ - Worthy of a mention, but Flickr is better
Video Hosting:
https://upload.video.google.com/ - It's google, it's fast, though there is a validation period for all uploads. My personal favorite
http://youtube.com/ - It's free, it's fast, nerds love, it's awesome
http://www.zippyvideos.com - It's pretty good, but gets slow at times, and limits at 20mb
http://www.putfile.com/ - It's quick, but I find it slow, and it limits to 25mb
Web Hosting:
http://hostiz.com/ - 150mb no ads!, great uptime
www.geocities.com - always has been around, pretty reliable and easy to use.
http://www.apachefriends.org/en/xampp.html - Got technical skills? Broadband? A computer? Be your own server, this program makes it pretty easy (Linux, Windows, Mac, Solaris) It's All FREE! And you can still use your computer for regular functions. Just a warning, it's a lot of work if you've never done it before.