I had never used flickr, but I often use Snapfish, Photobucket, or the Kodak Picture site. These are all great tools for photo sharing. For me it is nice because I have family and friends who live all over the country and I often want to show them a picture or group of pictures, and it's really just not realistic to print them out and mail them.
Professionally the only time I really use photo sharing is when I am directing one of the school plays, I take pictures at rehearsals and the performances and then I save them on my work computer. The only time they are then shared is if the school wants to put them up on the school website, or a parent asks for some of them. In the past I have always just emailed pictures to parents, sometimes we do it as part of a fund raiser and we sell the pictures. But I have never put them up on a photo sharing website, because it has always made me kind of nervous, even though I do have parents sign a specific permission slip allowing the pictures to be used. This is definitely something i will consider for next year though. It might be cool to do a an album from the night of auditions to the last performance. Although I think maybe doing that through a Theatre Dept. Wiki or something would be better. This way I could also post a rehearsal schedule. I think especially being a young teacher, I have to be extremely careful though when it comes to sharing photos of students.