These are a few apps that aren't necessarily flashy, but provide functionality that in many cases I'm surprised is not standard in the Android OS, or provide much improvement over stock Android apps
Dialer One -- a much more flexible dialer, make sure to go into settings to find a setup you like
NotCallLog -- takes you anywhere but the call log after a call, like the home screen
Handcent SMS -- so many more options than stock, including messaging to groups
xScope -- much better web browser
Astro -- file manager that lets you create shortcuts to files/folders on your homescreens
Profiles/Quick Profiles/Setting Profiles/Quick Settings -- or some other way to easily control all the different volumes, screen brightness, etc. Also, make sure to add the stock power control widget to your homescreen
Ring Guard -- Prevents your ringer volume from accidentally changing
myLock -- Lets you skip doing the whole slide-to-unlock thing
Swype/HTC Keyboard -- These keyboards aren't in the Market -- search the forums or Droid-Life for the .apk files that you can install using Astro
Apps Organizer/Folder Organizer (paid version of Apps Organizer) -- Create shortcuts on your home screen to groups of apps and you'll never have to go in the App Drawer again.
Home++/Helix Launcher -- Slightly more advanced, but both let you add more than three home screens, and give you a "dock" that's constant across all home screens