I don't mind random battles so much. I do agree that they can be a bit annoying, especially when you are just trying to get somewhere, or solve a puzzle.

I sure enough love random battles.
Most of the time, they are part of the gameplay, so they shouldn't be removed.
Then again, I'm part of those that find most JRPG too easy, so I think there's a strong link between people loving or hating random encounters, and the way they play JRPG.
People that play JRPG like they play WRPG (which are nearly all munchkin friendly) usually get their ass handed to them because of a mere random encounters they didn't plan for. That's my theory at least. Which would explain why they hate them. Especially since most games with random encounters have both a flee option and some items reducing the number of random encounters, or even removing them entirely.
I can't remember a JRPG I played that didn't have these options.

I never use the flee option, unless it gives me a reward for doing so, like achievements for example.

Me too in dungeons. 

Putting monsters in dungeons that you can't possibly avoid kills the whole advantage of having on-screen monsters.

I got used to games like Chrono Trigger, and then when I moved to FFIV DS, it was pure hell at the beginning... Although, I'm used to them now.

But... when I'm trying to get to a treasure chest it's just annoying to have to fight 15 different battles on the way.