Do you find them annoying, do you like them? I personally don't like them because it kills the exploration mode of maps in some games.
I like it because it breaks up the monotony but I admit that after a while it can start to feel very tedious and annoying. I don't mind that it is part of the game as long as I am given an option to exit when I want to.
As long as there aren't too many random battles I don't mind them, they add depth to the game instead of all the scripted ones. I played games where there were a lot of random battles though, that got annoying pretty quick.
Eh if other players pose as a challenge then why not right? It's a game and people want to prove their mettle. Leveling up can be boring and tedious that's right so engaging in battles once in a while can break that monotony.
I think it just depends on how well they are integrated with the game. A lot of early RPGs used random and meaningless combat as a way to extend the play-time of the game... and usually they felt very artificial and a nuisance. But I do think random attacks are important in a gameworld just because they add some unpredictability and randomness and do not allow the player to pre-plan every action.
I'm not against random battles personally, but it depends on a lot of factors. How frequent they are, how annoying the battles actually are etc. They can be done well, but they often are simply used to pad out game length which is why I prefer having the enemies roam the map which is better than random battles by a large margin.
I'm OK with them, but it gets annoying when they're too frequent or there's no way to control them (items/equipment that lower/raise encounter rate). I prefer semi-random though, you know? Like Final Fantasy XIII-2 is a good example: enemies show up randomly BUT the way you react to the overworld encounter lets you get a surprise attack or avoid the enemy altogether, so it's not completely random.
I agree with this post, and I'll say that my favorite kind of "random battle" system is when it's not actually random and the encounters are designed by the developers themselves when balancing the entire game. Think of Chrono Trigger for example. I really like that way of doing monster encounters in RPGs.
It depends for me, on one hand they can help level up your character. On the other hand it makes the adventure a lot more tedious.
If the random encounters are too frequent, the battles can get very annoying, very fast. Overall, a very 'meh' feature at best, that I can live without.