I watch them because I either can't play the game myself (yet want to know how it goes), or I want to see what the game is like before a purchase (in which case I'll look at maybe a couple videos so as to not spoil too much, if anything). I also enjoy informative commentaries, where the LPer knows what he talking about. Funny commentaries are a bonus, but not a necessity.
I also sometimes watch LPs of games I have played and completed, to see how someone else plays it (and to hear their comments on it).