I have played many MMOs in the last 5 years or so, both open-world RPGs an lobby-based types, in all kinds of setting (sci-fi, historical, fantasy).
These ones come to mind whenever someone asks for a recommendation:
EVE Online -- By far the best of them all because of its sandboxy nature and how each action has meaningful, realistic consequences. There's a reason why even after 10 years, EVE playerbase still grows to 500,000 subscribers (Feb 2013 figure).
Things you can do in EVE Ship size comparisons in EVE$4000 Titans in EVEWorld of Tanks -- If you like tanks, chances are you will like this. Imagine 15 vs 15 Counter Strike match, but each team member is a WW2 tank/tank destroyer/self propelled gun, which has to factor in terrains, shell penetration, armour facing, speed, etc. You see, this game is much more tactical because each tank has its own characteristics, making teamwork essential. I'd suggest you check out our World of Tanks thread; plenty of Bay12ers playing it. I'll let this gameplay video speak for itself:
http://www.youtube.com/watch?v=FXKS6bfXyysWar Thunder -- Similar to World of Tanks but it features WW2 planes instead. This one has a lot of potentials and will feature combined arms battles (planes, tanks, ships). I've been making a transition from World of Tanks to War Thunder.
Worth mentioning (just haven't had the time to play it enough):
Planetside 2 -- Battlefield 3 on steroid. Imagine 1000 vs 1000 match in a single server, with infantry, land- and air-based vehicles. Has its own active Bay12 thread, so yeah it's popular here.