I've used Photobucket (free, not pro) for four years without a single problem whatsoever, and it makes it very simple to keep all of my stuff organized.
Imageshack, on the other hand, loads slowly most of the time, and has a tendency to remove photos after they've been inactive long enough, which makes it a poor choice for picture archiving.
Honestly, I don't know why the rest of you don't use Imgur. Maybe I've just been using reddit for too long, but it's the archtypical image hoster in my world.
I Dropbox absolutely everything. It's by far the most convenient method of image or just plain file transfer over the internet. I wub it.
For dedicated imagehosting sites, imgur is my next choice. I have a photobucket and I have an imageshack account, but the only time I've used either was when we uploaded all the faction section icons to my photobucket. Other than that, Dropbox everything.