My favorite apps:
New York Times
NPR News
Pandora (free "radio" based on themes or groups or songs you choose)
Relative Pitch (musical training)
100 pushups (oooh, exercise)
200 Squats (oh, no, MORE exercise!)
Netflix (watch streaming movies on your phone for free with Netflix account)
Free Books (all the classics, all free, and the option to read them on a black screen so no disturbance reading at night in the dark)
Louvre (the museum, just fun. And free.)
Patagonia (you can select sales, and even shop from the phone)
Tesla Toy (duuuuude, this app is AAAAAWESOME!)
Zen Timer (works great for naps as well as meditation times)
If you have access to a Costco, I really recommend an iHome device of one sort or another. (from $30 for a simple speaker/charger, all the way up to $50 for a speaker/charger/lamp or $80 for a stero speaker/charger/etc.) I have the basic simple speaker/charger, and plug my iPod into it probably more often than I plug it into my computer. My kid loves the thing, and will use it to charge in a hurry (since it brings the iPod up to full charge faster than the computer could).