Countdown (free) is one of those "I should thought of that" apps. It's simple in concept, but useful all the time.
Countdown has an attractive UI for adding upcoming events that are important for you to keep track of. A birthday, a vacation, a deadline for a payment... anything really. You enter the events into Countdown and can even pick an appropriate photo of a person or place to make the screen more useful or attractive. After that, you're done. The countdown clock starts timing months, days, minutes, even seconds if you like, until the event.
You can set reminders for each countdown, have the app play a selected tune from your library when an event occurs, or share countdowns on Facebook and/or Twitter. Yes, your iOS calendar and Reminders app keep you on top of events too, but I like that Countdown puts all the events in one place with timers, and you can order those events by date to figure out what's urgent and what's not.