Really, Random encounters suck. I hate them. They just get annoying, and like Link in Pink said, they just end up getting you killed because you either, ran out of items, or you just suck.
As for leveling, I don't mind it so much, as long as I don't have to level like 60 levels or something. I'm using Star Ocean 3 here. This is one of my absolute favorite games. I'm really a sucker for futuristic type games so this one really got me. However, there were points in the game where I had to level up something like 5-10 levels. I didn't mind though just because I would go overboard to something like an extra 5-10 levels to get that next really cool skill or something. But then I got to the final boss. I got there at like level 55 or so, and could not beat him for the life of me. So I went back and trained an additional 15 levels to around 70 where I was finally able to beat him. This leveling I don't like. You are right up to the final boss, and you can beat everything around you pretty easily, then you just get slaughtered by the boss. It just really depends on the situation.
For the characters, I like the characters that are not silent. Silent characters just irritate me. They have no personality whatsoever and it's really boring. As for the teenage kid stereotype, it's really a staple of RPG's if you think about it. I mean, if you look back at most RPG's, the characters range anywhere from 16-28 with characters around 19 being the most common IMO. I really don't mind the whole teenager thing here though, even though it is a pretty bad cliche because that is who the games are really aimed at. Kids like to play games where people like them get to be the hero. That really adds to funness if you will. Once the kids turn 16, 17, 18, ect, however, they don't care about that anymore and really look for a good thought out character that fits the storyline and that part right. I mean, a 15 year old who is the absolute best at swordfighting in the world, (who then doesn't have any skills, HP, MP, or anything like that...) just bugs me...but that's another rant for another time...
Another thing that I don't like is when the battle system involves just button mashing. Now, Star Ocean didn't completely comply with this. I mean, you run around on a battle field and press x over and over again. I mean, yeah, it did have some tactics to it with the skills and such, but once you mastered those, it just turned back into button mashing. A battle system that I love is one like Advance Wars, where you actually have to think about what you want to do. The only problem, is how difficult that that system is to integrate into and RPG. Yes, it's possible, but usually you have to revolve around a bigger party and bigger enemies which ends up being more work for me. The XAS system is an OK system IMO because, yes you can just button mash, but that really can just get you killed.... A bad battle system really throws me off of a game. A bad battle system really lowers the gameplay value which then in turn, makes it no fun.