Depends. I don't watch walkthroughs, I only ever read them if it comes to that, because I'm still kind of doing it myself that way, and I can also skip only to the specific action/part I'm not getting.
Watching a re-play of myself playing a game will make me suicidal because of all of the potential parts where I was dicking around; should have seen something coming; walked right past an enemy in the other room; etc. However, I enjoy watching short replays of my badassness; funny/crazy stuff that happened, usually in sandbox games; and final killcams though, because they can make conversation topics with friends, and stroke my ego.
I enjoy watching Let's Plays from people I enjoy. Like, say, Graham and Paul. I also enjoy shows like Unskippable. And Loading Ready Run in general. (/fanboy)
I don't really enjoy watching other people play games just because on the internet; but I sometimes enjoy watching people play games in person, usually if they're my friend. Like someone else said, it's usually because conversation, especially about the game, is happening constantly. I usually like action games (See: first person shooters; anything from Bethesda) and sandboxes that are actually fun (See: Grand Theft Auto games; again, Bethesda; Just (be)Cause 2).
And although I'm not the kind of person who's interested in those kinds of games, I guess watching however many people play, say, a fighting game, especially if they're really good, could be enjoyable.
I don't know what to put for the poll, so I'll just put Let's Plays. Tack me down as a technical for anything else applicable, though.