I'm going to tell you about the browser based MMORPGs, but there really isn't anything exactly like runescape (Runescape has a very particular java engine).
To play games in flash, there are Dragon Fable and Adventure Quest (In both you have to pay to have full access to the game, and notice that Dragon Fable is still under construction and that it's hard for non-members to login into AQ). There are also those community based flash games (that some people consider to be MMORPGs) that are becoming really popular: Gaia Online (that I already played and that is really cool), ClubPenguin, PuzzlePirates, and i think that Habbo goes the same way; in all of this games you create an avatar and play games like fishing to get money and personalize those avatars.
There’s also the pure browser based ones: Tibia is a fairly popular game, BiteFight and Knightfight are OK. Travian is a strategy MMOG, also pretty good. There’s also pokemon crater (but it has a lots of publicity) and, my personal favorite, FallenSword (it’s much like pokemoncrater, only that it doesn’t have lots of publicity, and has a guild system that stimulate interaction, not to mention the lottery and the auction system).
Have fun.