I've been using Photobucket since I started on the net and I've never had a problem with it. Except for that one phase where they decided to scramble all the image names you uploaded for privacy reasons or something. That was ridiculously annoying.

In between I've used Imageshack and tinypic. Imageshack has changed now and wants you to make an account, and tinypic is unreliable and they often delete old pictures/replace them with others which makes them a bother. So I've gone back to Photobucket again lately. I do use imgur to upload things that I haven't made myself but that I need a URL for, like official Pokemon art. I tend to keep everything I've made on Photobucket just because it feels more secure there and I can delete it whenever I want, too.