A while ago (a few months actually) I was thinking about the leveling system in Skyrim (because I really like analyzing Skyrim for some reason), and the thought occurred to me: Why have player levels at all? It wouldn't even be hard to remove them entirely - you get a perk in a skill tree every time you get 10 levels in that tree, and you get a point in each of the three main attributes for every level in a related school (warrior skills - health, mage skills - magicka, thief/rogue skills - stamina, following the paradigm already in the game.) This even ends up fixing a lot of the problems I have with Skyrim's perk system - the arbitrary level requirements for perks, with a bit of retooling, the tendency to never put perks in certain trees because of game balance (I'm looking at you, speech), and probably a few others I haven't thought of, while simultaneously having an absolutely equivalent result to the current mechanics.
I've never actually really liked the idea of discrete 'levels'. It just feels so arbitrary. I've always appreciated the Elder Scrolls' 'get better by doing' mechanics, and they make it extremely easy to get rid of player levels entirely - although it'd be a lot harder for most RPGs.
In any case, let's take a look at what player levels do for you. They give you a very tangible goal and reward, usually a fairly substantial step straight up, maybe some sidesteps. This allows the player to gain a sense of progression, sometimes to ridiculous degrees - how many JRPGs have you played where you start out dealing double digit damage and end up dealing hundreds of thousands every hit by the end? It separates controlling your character's skill progression and actually playing into discrete chunks, letting you optimize your build.
The big cons, in my opinion, are an encouragement of grinding (a practice that should be a capital offense in any competent RPG, in my opinion. THOU SHALT NOT REQUIRE GRINDING) and a total disconnect between actions and progression - 'Oh, you just hit some arbitrary milestone by mining that rock or talking to that dude? I GUESS I'M BETTER AT KILLING PEOPLE NOW!'
The pros are ease of design and balance, because it allows you to be MUCH stricter with player progression, and increased precision of progression for the player. It's much harder to metagame a skill-based rather than player level-based system, I feel - a con for some and a pro for others.
I'm not saying that getting rid of player levels is something every RPG ever should do, but I think it's surprising more haven't experimented with shifting the emphasis away from them, especially considering the runaway success of Skyrim. Perhaps a new breed of RPG is coming? (It usually is)