It's rarely ever completely DOWN, but sometimes it'll lose stuff for a little while as they move things from server to server.
Big sites like Flickr aren't just one box, but have a distributed server network where each server (or farm of servers) is like a cell. If one goes down, there are redundancies in place to pick up the slack.
These things take time, though. Flickr is one of the fastest growing sites on the 'net, so I give it a little slack.
MySpace is down or broken very often too, but it was originally built by two knuckleheads, so it too gets a lot of leeway in terms of being forgiving of its hiccoughs.
I have noticed, though, that Flickr is often not down for me when it's down for other people because I'm a paid user. That does seem wrong, but I can't really complain.
I use it for the social aspects and as a way of offsite storage/backup for my photos. $25/year gets me 2Gb/month of transfer, and I don't think I can take enough worthy photos to upload in a single month, so I'm good. There's no limit to how much you can store (other than 2Gb/month) so you could have hundreds of Gb up there in just a few years.