Almost every android user will have their own top 10 list depending on how they use their smartphone.  It will also most likely change from time to time.  A truly useful android app will be one that you use regular over a long period of time.  Here's my top 10 list:

K-9 Mail is a POP3/IMAP capable email client for the Google Android.  It is community developed freeware.  I like to configure it with IMAP so the messages stay on the server for later viewing in my regular email client on my PC.

gReader - Google's news reader allow you to keep up with any blogs you may follow while not around your main computer.

Advanced Task Killer - Always available in the status bar, ATK can be used to terminate renegade programs that don't want to close.  This can also help save the battery of the android device.

Wi-Fi Switch - is a status bar switch that toggles WiFi on and off.  No more fumbling through a bunch of settings to turn on WiFi.

Weather Bug - downloads the current weather and forcast for the next several days.  I like that it displays the current tempurature in the status bar.  Any weather alerts and an alert icon also appears in the status bar.

EasyTether - I did buy the pro version of this.  In conjunction with a driver installed on your PC this application allows you to access the internet via your android phone.  May not be the fastest, but still useful if needed.

ShopSavvy - This application makes comparison shopping extremely easy.  Scan a UPC code on a product and it searchs the internet for the product available online and local and gives you the price.

Libra - tracks your weight for you.  You can enter a goal and it will graph your progress towards that goal.  Very easy weight entry, the first time you run the app each day it display an easy dial with your last weight already selected.

Analytics Widget - I have several web sites that I like to see what sort of traffic they are getting and this widget is nice for doing that.  I have several placed on one of my android screens that monitor different sites.

Robo Defense - A guys got to have some fun.  This is an addictive game, so much so that I did purchase the full version so I could play different maps and advance to more levels.