I'm not using Flickr but I'm really happy with DeviantArt. There is no limit on how many pictures you can submit. Besides, you can put there not only pictures but practically everything else - poetry, short stories, videos, paintings, everything.
What I love about DeviantArt is that everyone has a place there - beginners and professionals.
But of course, you might want to stick to the site you've got used to. That's petty understandable. :)