A friend of mine had this problem, and asked me to try to help him out.
After he logged on to Yahoo Messenger, the Messenger disappeared. Just plain and simple "closed himself" :)
I looked into it, even opened the Task Manager, and saw that the application just vanishes from there too.
I had no idea what to do at first, but I saw some forums saying that it was a virus, or something like this, related to the PC-s safety.
People was saying about using Hijackthis and stuff like that.
What I did was: installed Spybot Search and Destroy. Ran it once, found 18 problems. I never even checked what was all that, I just clicked on "Fix selected problems". Problem fixed ;)