http://www.battleon.com/Adventure Quest. Flash based, single player with some minor other player type stuff thrown in. I like it as it has many humorous geek type jokes thrown in and its one of those games that you can play it for 5 minutes and then turn it off or go do other things types of games. My favorite type of game when you need something to do for a short period of time while you're waiting at work for a report to finish compiling or what not.
Character never gets deleted; I made one 4 years ago, and hadn't touched in over 2 years until just recently and it pulled it right up right where I left off. They make money by offering people to give them a one time payment to upgrade their account to a 'guardian' level type thing that allows their characters to go to special places and get better items, but it's completely playable without paying them. Back when I first made an account it was when they were first starting out and the guardian account was a simple paypal 5 dollar transfer, so I got it and it was worth it for all the content and little perks that it gave me over the years and will continue to give me as again, it was a 'good for life' type of deal. I'd imagine nowadays that it is probably a bit more since it seems they are decently popular now, but like I said, the game's completely playable and enjoyable without it as well.
As far as I know, this is one of the only flash games that is technically a browser based MMO with full online multiplayer.
http://www.aq.com/ The same game as I described above also has a MMO version. Pretty sure its based on Flash, but I've never played it.