I only have a few non-Apple apps in my dock:
SoundCloud (Mac, iPhone) by Robert Böhnke
Nice tool for discovering new music. Loads quickly. Simple interface. Apple needs to copy Soundcloud's touch-to-seek feature. Much faster than scrubbing. (to find the part of the song you want to play)
Time Out (Mac) by David Sinclair
Gently reminds you when you've been spending too much time staring at the screen and need to take a break.
Swackett (Mac, iPhone, iPad) by AGLogic
Different type of weather app. Tells if you need a sweater, jacket, or coat when going out. So you can grab what you need and go.
All of these are free, though I'm planning on buying the next version of Time Out, partly because it will let you customize the image that pops up for break reminders.
Have an unusual app in your dock? Sound off in the comments.