I definitely played some Minecraft because of Achievement Hunter's weekly minecraft let's plays that I used to watch.
While I typically don't watch streams/let's plays in the vein of playing through a whole single player game(since I much rather just play the game myself) - multiplayer stuff or creative stuff can be pretty fun to watch. It really depends on the streamer. Robbaz builds crazy stuff in games like From the Depths or Kerbal Space Program and does stuff that I will never come up with or have the patience to do. Likewise some multiplayer streams can be fun to watch since they might play a game that my friends are not interested in playing, nor would we have the same sorta interactions. I also enjoy watching Starcraft 2 videos, watch some pro games and am a fan of Florencio who basically just does crazy builds and fucks with people. I am personally absolute trash at SC2 and can't find it in me to go practice and get better at it.
I typically don't buy and play those sorta games though. Since I very much enjoy watching them more than playing them.
Some multiplayer streams also help me get a good idea on whether a game might be suitable or fun to suggest to my friends to play together on.
I do sometimes watch streams or let's plays of games I already owned and played, just to see how others might react to them. But this is kinda a reverse. I watch stream because I played the game rather than buying a game because of a stream.