Are you talking about native apps or web apps? My favorite web app would have to be Facebook.com and my favorite native app is really a toss up between AIM and Spore (the video game). Since they are both in different categories, I will choose both as my favorite.
I've always loved the animated weather app on HTC's 3D flo so I bought last night for $0.99 and I love it. Only wish it had world weather but it is only for the states.
Hard to say what my one Favorite app is, but here are ones I use often enough to call 'favorite' and most are on my first page of apps:
OmniFocus (to me only makes sense if you have the desktop software though)
Twitterific
Google
Facebook
NetNewsWire
WeatherBug
Sportacular (it's good but there has to be better out there -- any good sports reco's from anyone)
MLB At-bat was great during the baseball season, will definitely be spending that money again
Shazam - if I am driving and hear a song on sirius radio that I like and want to remember to look up in iTunes I just have Shazam tag it and review them later
Bloomberg
Just downloaded Pocket Express - used that on my Treo 700w before so that holds a lot of promise.
I am very fickle on the games. I play them for a bit then find a new one. I don't think I have really 'finished' one game.