To organize contact info and dates, I use a combination of the built in Calendar and Contacts apps, as well as one called Occasions. For login/password info, I have mSecure. It can sort all your online ID/password information, categorized by type or name.
I have some travel apps, such as Gate Guru, Flight Update, and Packing, so I can find ways to kill time at airports, keep updated on my flight status, and pack efficiently, respectively.
I also have Lose It for weight loss, which I use in conjunction with Convert measurement converter and Fast Food Cal to see calorie counts from chain restaurant foods.
Quickly going through my screens, I have the ones I mentioned plus Opera Mini (I don’t use Safari), my bank’s app, Meebo and a free text message app, Solitaire and Bejeweled, ESPN ScoreCenter, NY Times, Flixter, Pandora radio, a wi-fi finder, IMDB, Amazon.com, a Marvel comics app, a LA transit map, a city map app, a mall directory app, a lunch truck GPS locator app, Urbanspoon restaurant picker, USPS’s app, and the Apple MobileMe app.
I’d say 3/4 of them were free. The flight tracker was $4.99, Bejeweled and mSecure were $2.99.