I'll recommend imgur. It also has unlimited bandwidth and storage and you can also edit the images before and after they've been uploaded.
The images won't get deleted if they've been accessed at least once in six months. And this is all with a free account. You can also upload without an account too. The limit for image size is 1 MB (5 with paid account) I believe (which means reeally high res jpgs are allowed, they don't get resized... if you try uploading a non-animated image from 1-10 MB it gets compressed and/or resized to fit under 1 MB). And also the images themselves are up even when the site itself is down.
For (free) larger gifs or something like that (several MB) there's minus.com
Edit: They've changed the image deletion time to 3 months now though.