I have recently started playing flash games on facebook. It is awesome because you can see how your high score ranks against all of your friends. It is a new way to get the classic arcade high score action. Here is some of the games I have been playing (you need to be logged on to facebook to play).
Pixel Ranger - Run and shoot stuff just make sure you don't run out of ammo.http://apps.facebook.com/pixel-ranger/
Bejeweled Blitz - A one minute version on bejewled (match 3 of the same colored gems). http://apps.facebook.com/bejeweledblitz
Waka-Waka - A pac man clonehttp://apps.facebook.com/waka-waka/
I seems like games on facebook continue to grow in popularity. It amazes me that so many people are playing farmville/ mafia wars/ bejeweled blitz. Seems like there must be tons of casual gamers out there that would be interested in arcades if it was presented correctly.
Facebook isnít just a best communication tool for you, your friends and colleagues, it is great platform for excitement and fun. Since Facebook created possibility for developers to make their own apps they have created really creative and funny games to play together with your friends.