I thought I'd hate them at first, because I don't like things happening suddenly, and I was a lot worst when I was younger (for a time, I would play FFVII with the sound down, but I thankfully stopped doing that, because the music is awesome). I actually don't mind them for the most part, and find them to be part of what makes an RPG an RPG for me.

There are sometimes when they get annoying, I will admit; like when you're trying to workout what you're doing, and then a Random Encounter distracts you, or if the music in this particular place is really good (I really wish that Zozo in FFVI could have "Slam Shuffle" be the music throughout, including during the battles, because I love it, and I don't like the fact that the Random Encounters interrupt it).

Also, is it me, or does FFVI (and maybe the other games, I'll check) seem to punish you for going the wrong way with Random Encounters; It seemed every time I took a wrong turning, I'd get a Random Encounter the second I turned back...