Rosetta Stone language apps. Just enough to make you think you can actually learn the language, and only 99 cents each.
USA Manual and Presidents, know your country, well, if it is your country. Other countries probably have their own apps. If not, they should.
The Elements: Fun facts and pictures of the elements. The most beautiful table of elements in the known universe.
Star Walk, just where is your sign anyway?
Knot Guide HD, for those times when you have to explain what you meant about being all tied up.
KhanAcademy (for iPhone, but worth it anyway. Can also be found in iTunes U) This one works slightly better on the iPad than the Khan Academy, even if they have the way cooler icon. Free lessons for just about any course you slept through from grade school to first year college.
iScience, for the math formulas you've forgotten.
ArtRage, what kind of renaissance man can't paint?
Seline HD and/or Garageband think of them as a modern day lutes, with training wheels.
TED or TED+SUB, be familiar with some of the most forward thinking and creative ideas in the world.