My top apps (For my tablet), in no particular order.
Art
Sketchbook Pro - Best current drawing software on Android. Still needs a lot of work and polish though. Has pressure sensitivity support for my Thinkpad and other N-Trig devices.
DSLR Controller - Remote control over my 500D, with live view, remote shutter release, image review (can view raw), and control over just about everything. Currently in production and so is significantly reduced in cost (buying now retains your license for the full version.
XDA thread)
Photoshop Touch - A respectable attempt at a touch version of PS. Currently very limited in toolset. More than worth the asking price though.
Utilities
swiFTP (free) - One click access to my tablet's storage over wifi. Invaluable.
ES File Explorer (free) - Most desktop-like experience. Access to internal, external storage, dropbox, and ftp servers.
Unified Remote (free) - Remote control of functions on my computer over wifi. I watch hulu and movies on a TV via HDMI out on my computer and am able to use this as a virtual mouse and keyboard.
Teamviewer (free) - Best and most fully featured remote desktop control client.
Handycalc (free) - Graphing calculator that uses keyboard input. Has other function like easy unit and currency conversions.
Hacker's Keyboard (free) - For when I need access to desktop keyboard keys that aren't present in most android keyboards.
Thumb Keyboard - My general use keyboard. Arrow keys, macros, and many more functions. Highly customizable.
Media
VLC (free) - Plays anything better than mobo or mx video player, has a better UI, and is not even an official release. The actual release is bound to be insurmountable.
Player Pro - Was the most stable music player in my testing, and has nice playlist/file handling.
Cool Reader (free) - For reading any eBooks you can't get from kindle or google books.