I'm an Android convert. Direct my downloading power at free applications.

[Agnostic Bear]

Need some of those them here essential apps please.

[Recursion]

First of all, you better have rooted that phone sir. Second of all, welcome to Android, iPhone sucks ****, yes I'm a fanboy.

Shazam - Music ID
Twidroyd - Best Twitter client ever. Srsly.
Facebook
Spotify - If you haz premium
myPlayer - iPlayer streaming
Boxee - A nice little remote app for Boxee servers
SetCPU - For overclocking/underclocking, needs root
Quadrant - Benchmarking
Barcode Scanner - QR Codes are the new craze yo
AndFTP - You can guess
Adobe Reader
DocsToGo - Powerpoint, Word, Excel
APKTor - Get some repo's, free apps for all!1!11!1!
ConnectBot - SSH app
drocap2 - Needs root but awesome for easy screen caps
Google Earth
Google Sky Map
Google Translate
MSN Talk - Best MSN client out there for now
Package Tracking - Good for the major couriers
Photoshop.com Mobile - Good for on-the-go image editing
ROM Manager - If you're rooted, you'll love it.
XBMC Remote - Pretty much what it says
Wardrive - Wardriving ftw
Wapedia - Awesome wikipedia client
Stats
Shark - Outputs to a .pcap file for Wireshark, good for WiFi sniffing, needs root.

Just a few, some paid, some free, you probably won't use half of them but I do so meh :P

[Shar]

I might check a few of those out, thanks!

[Dentafrice]

Everything they said.. few other things I use...

TempMonitor - monitors battery and CPU temp.. useful when overclocking...
HandcentSMS - very customizable SMS interface... way better then stock I do believe.
Grooveshark
Pandora

Alchemy - fun game to combine elements, see what you get.
Astro File Browser - basically views your entire SD card / phone. Great file browser.
BatteryTimeLite - Monitors battery good.

Last.FM
MeeboIM (Facebook IM)
Mobisle Notes Free - Great for keeping quick notes / checklists
Save MMS, makes it easier to save all your MMS.
SpeedView - Speedometer, uses GPS to see how fast you're going.
Task Manager

Uninstaller

Where's My Droid
WiFinder

[JACKTARD]

Games...

Throttlecopter
Goldminer
Abduction
Replica Island
Shoot U!
Air Control Beta
Fish Food
Crystallight Defence

Applications...

Net Counter - Useful to check you dont go over your data usage
My Tracks - Uses GPS, record tracks... tells you a load of stats and graphs and uses google maps to show where you've been too :)
Bump - File transfer with other android devices and iPhones
Shopper - Take picture of front covers of stuff and it brings it up in google shopping
Advanced Task Killer
Google Sky Map