Edit: Okay, here's some stuff you'll probably want to check out any way:
- Swype keyboard: You might have heard of this one, you can either touch type or slide your finger around to type.
- Taptalk forum app: It's an app that lets you browse many forums (like this one) in a mobile-friendly format, which will spare your data and load stuff quicker.
- Google Chrome to Phone: Allows you to instantly send files or links from Chrome browser to your Android (check Fox to Phone extension if you use Firefox).
- Google Goggles: Basically a photographic search engine, you snap photos of anything from barcodes to book covers and it Googles it for you.
- Plume: In my opinion the best Android Twitter client, lots of features and nice looking widgets which the native Twitter app is missing.
- Winamp: Like the name suggest, it's a music player which has WiFi sync with Winamp on PC. Lots of people prefer PowerAMP because it has EQ settings, but it's not free.
- Notification Notes: It's like tying a string around your finger, it lets you jot down notes like so many other apps, but this one places them in the notification bar up top as a frequent reminder.
Those are the ones I install first and use the most... other than that, just peruse the categories in the Market app or check out sites that do Android app reviews.