Post them here, I'll start. Please try to indicate whether the app is free, ad-based, pay, donate, etc.
Google Sky Map (free) - If you don't have this or haven't tested it out, its completely badass and a great way to Wow people.
Handcent (free w/ unobtrusive ads, paid option to get additional features) - Very customizable sms texting application
Battery Left (free, pay) - Nice looking battery widget
Beautiful Widgets (pay) - Fantastic clock and weather widgets. Well worth the money, imo.
Circle Battery Widget (free/donate version) - minimalist battery widget
MotoTorch (free/donate version) - Let's you use the camera flash as a flashlight and has a convenient widget so you don't have to actually open an app to use this. I use this all the time - make sure its compatible with your phone
Kindle (free) - great if you read Kindle e-books
Tapatalk (free to read posts/pay to be able to post) - Great way to read the Shag on your phone - much easier than using a browser. Pay to be able to post.
Dropbox (free) - great if you have a dropbox account that you need to access from mobile devices
NewsRoom (pay) - pretty slick rss reader
Dolphin HD (free) - great alternative to the stock browser
Our Groceries (pay) - syncs with iPhone version - not a slick UI, but effective and lets my wife and I update the grocery list on both of our phones
These are just a few that I use that I'd recommend - most are pretty well known already.