I use Flickr, Imgur, DeviantArt and TinyPic depending on what I want to do with the images.
Tinypic makes them terrible quality, but if it's a cell phone pic that I'm just posting here, I don't care. It's also nice for screenshots.
Imgur has a limit, but it's the easiest one to use if I'm going to be putting it on Reddit.
Flickr lets you keep them high-quality, but there's also a lot of image theft because when people look for pictures, that's the first place they go, and Wikimedia Commons has bots that collect images from Flickr, and they stay in Wikimeda Commons even if you change the licensing on the image...and odds are most people using the images don't actually go to the source and make sure it's still under creative commons.
I don't use Deviant Art much anymore, but I used to use it for more artsy/professional photos. Not cell phone snapshots, just images I felt were either really nice to begin with, or that I put a lot of effort into editing. It's kind of a hassle posting there, which is why I don't use it much anymore. But it is a really good place to get feedback/critiques.