I can't say that a mini-game has made me like a game more by simply being there, but mini games (especially when they can lead to bonus non-obligatory content) can be a nice change of pace.
However, a lot of mini games in games today are either part of a meta required to take part in to maximize the potential output of the game (like adding poker mini games allowing you to make money to bypass a lot of other problems), or they are time wasters that are added to the game that stop you from doing other things that time-slot instead causing you to risk missing out on content.
That said, I think it's nice when developers try to do novel things with their games. It shows that they have fun with the process.