I always took random encounters for granted, so they never bothered me. I do like games that don't have random encounters, though.
While we're on this note, I have to say that I'm getting annoyed at the trend of having a lame music for the final dungeon and it still having normal battle musics. You don't have to make every battle play a boss theme or something, but a battle music that sounds a little more serious would be nice. As for lame final dungeon musics themselves, not too many final fantasy games have this, though Final Fantasy II comes to mind. However many other games are going out of control with having some bland, boring music for the final dungeon [like Star Ocean 3, 4, and Valkyrie Profile 2].
I think this is branching too far off-topic, but I have to establish my annoyance with games in general that have really lame normal battle themes. Seriously, I don't think they even try with some of these, as 99% of them sound like some crazy waltz in the park.