well lets see, I am not gonna list them all but I will cover my most used.
Appbrain - Must have.
Dolphin Browser - This is REQUIRED. Best internet app out there
Twidroyd - Best twitter app
Calorie Counter - I count my calories and this makes it very easy. I use this all day
Jorte - The best calender I have found, Awesome widgets too.
Pandora - Enough said
ShopSavy - Barcode scanner and helps you find good prices, cant beat that
ebuddy - If you use any IM program this is good, I use it for facebook, AIM, Gtalk and yahoo chat.
Alarm Clock Plus - Best alarm clock out there and it makes you do math to turn it off.
Droidfit - Keep track of your workout
Aldiko - Best ebook reader
Also for file explorer i use
Astro
ES File Explorer
and for security
Lookout
Where's my droid
Edit: Forgot to mention games.
Free Games:
Cestos, Homerun Battle 3d, Super K.O. Boxing
Paid Games
PSX4Droid
and all the other emulators