Here is a list of some of my favorite Facebook Apps:
FriendFeed: Allows me to publish my life stream on my Facebook profile
Boost: Boost is a Firefox add on that allows you to change the look and feel of Facebook. Adds a bunch of cool functionality like “download whole album” and showing full size images when you mouse over them.
Nexus: Creates a graph of your network. Really interesting to see how you are connected to other people and how connected they are to your friends.
FBcal: Generates an iCal file of your upcoming Facebook events and/or upcoming birthdays. Seeing as my Google Calendar plans my life, I don’t know how I’ve lived without this application for so long!