I used to play World of Warcraft, which is really fun, but I am not the biggest fan of the latest updates, so I haven't played it for a while. These days I focus my time on scrolling through the free to play games on Steam. Happy Wars and Tom Clancy's free to play game are my favourites at the moment, definitely a lot of fun!
I don't play it anymore but it does remain a favorite of the free mmo kind of games from various sites. Wartune. It was a nice community in the realms I played in so long as it wasn't a website that made a new realm each month. There were helpful people who wanted to work together to improve their characters. I just got burnt out on the fact that if you don't cash on the game you have to be there pretty much 12-16 hours out of the day in order to complete your events and get your rewards. When if you don't you fall further and further behind those around the same level as you.
Alternatively the other strategy is to play the game less than an hour a day and park your character, level up as slowly as possible and focus on getting gold/items max enchanted/astrals to high levels over anything else. And mainly do world boss and pvp events only. I found myself unable to do devote myself to any of the methods (money/time+/stall) so I usually fell behind or wasn't as geared as I could have been because I wanted to keep leveling. It's a good game if you can properly follow a method to success.
Kingdom Rush was probably my favorite flash game. I liked it so much that I've actually played it two different times, which is something I can't say for many games.
Recently I have been investing a lot of time in Runescape. Just the usual grinding to level up my character to decent stats before I pay to become a member. I'm also spending more time than I would playing games through Facebook. I guess it's the perfect set up. You can chat and play at the same time. I really enjoy games which I can play with my friends. Unfortunately, even though it is an MMO, Runescape can get quite lonely at times since none of my friends play it. Also if you play at night time, which I usually do, most of the people you will encounter speak some language other than English.
There's so many internet games out there. If you're talking about downloads, then i really like League of Legends. I've mentioned in another post that I've been playing since Season 2. It's a lot of fun to play because you can easily invite your friends and have them play with you in normal or ranked matches.
Dota 2 would be my choice for favorite game, but only when you're playing with 5man team, because the community on dota is really a toxic and cancer-like.
That's hard to decide, but I guess my favorite internet game has to be League of Angels because I play it so much. I occasionally play the Facebook games too.
Also if you play at night time, which I usually do, most of the people you will encounter speak some language other than English. 
