It depends on what you're looking for. For example, if you have elementary-middle school aged kids, whether they're your kids, a niece/nephew, a cousin, grandchild, etc. and you want a game to play online with them then I'd suggest one of Kingsisle's games, Wizard101 and Pirate101. Both are good for playing with kids under the age of thirteen and are really fun too. If you want something more mature, though, then perhaps World of Warcraft or any game along those lines.
With MOBAs, I don't really know much. The only one I've played is League of Legends, which is pretty great once you get past the toxic community. But if you aren't big on PvP (player-vs-player) then You shouldn't bother downloading them.
If you a good browser-based MMO, then try AQ Worlds. It's fun to play and the NPCs and events are pretty hilarious. Be prepared for puns if you play it.
Oh, and if you like Lord of the Rings, feel free to try Lord of the Rings Online. It's pretty good, and a fair amount of it draws from the books and movies.