Just a quick list I made.
FarmVille (by Zynga)-
http://apps.facebook.com/onthefarm/Other than the fact that is likely the most profitable game on FB now.
As a sandbox game, it has no real objectives other than to earn the ability to decorate your virtual farm with more options.
It has led to numerous clones, including clones made by Zynga themselves like CafeWorld, YoVille, etc. It was also a
clone of another similar farming game.
Mafia Wars (by Zynga) -
http://apps.facebook.com/inthemafia/Instead of using Flash, it only uses HTML. Some of its more interesting features include achievements, trading, collecting, frequent new content. It has also inspired a lot of clones which are all very similliar.
Castle Age (by Jelsoft Enterprises) -
http://apps.facebook.com/castle_age/One of the better clones of Mafia Wars. It added cooperative play against limited duration enemies which sometimes involved over 200 friend and friends-of-friends.
WarStorm (by Challenge Games) -
http://apps.facebook.com/warstorm/A collectible card game on FB using Flash.
Who has the Biggest Brain? (by PlayFish, Electronic Arts) -
http://apps.facebook.com/biggestbrain/Make nice use of Flash to create a "brain training" game.
MindJolt Games (by MindJolt Games) -
http://apps.facebook.com/mindjolt/Quite a large collection on flash games that are integrated with FB to challenge friends' high scores.
Whirled Games (by Whirled Games) -
http://apps.facebook.com/whirled/Another collection of simple flash games.
Battlestations (by TYLER Projects) -
http://apps.facebook.com/battlestations/Singapore's first Facebook MMO, with a monthly sales of over $50,000.
Any others that you think that are worth mentioning?