(I kinda skimmed so if this is repeated info I apologize)
There are a few games that vary the whole leveling process, or lack thereof. Some of them are really cool. Secret World (an MMO) skipped levels and went with a skill system. Everything was based on skills and weapons you picked and you didn't level in a traditional sense. Starting new skills put you somewhat back at zero. I never got too in-depth with it because my computer at the time sucked so running the game was sketchy. The downside being maybe you could max every skill? I'm not too sure.
Then you have the mentioned Diablo 3. Level to a cap, then a massive paragon level system for stats/perks. That works well for a grindy game like D3 with no real endgame but % stat better gear or timed dungeons.
DC Universe Online is kind of cool in that after level cap you just gain more combat rating. Each new expansion of content has a higher CR but no new level cap. The problem there is it's hard for a newer character to get to the point of a "max" character.
I would really like a system like Secret World. Sure baldrics were awesome to wear but just because we had Hunter Greens doesn't mean we all wore them. With so many flavor baldrics like yellow MMBs the point of a level baldrics was kind of moot once you earned a set. I collected them mostly for MECH uniforms and not prestige items. Going off of skills though gives you a chance to really customize your role in the world. Sure it's harder in a game like Realm where it's all medieval fantasy and not guns and swords, but you can pull it off since we also have magics.
I would love to be an Elementalism + 1H sword battle Mage. No throwing around daggers and casting a spell from EVERY circle of magic. Would I be at a deficit against pure ranged casters? Maybe, but that's my choice in play style.
I know people want to keep with the theme of Realm and stick to levels, but one of the biggest drawbacks that game had was people could just make a Giant Thief and macro Barracks all day long and get 1k using a DT and HoZ.
The skill/weapon system also helps with "twinking" a character with nice gear. Sure you can give them a super cool sword, but with no skill to use it it might as well be noobie stuff. At some point they'll be awesome but you can't start a new character, give him a rare dungeon drop and they go around one-shotting everything. They have to earn it.
Anyway, just my take on it.