Best calendar apps for iPhone: For when the built-in calendar app isn't enough

Looking for the best iPhone apps to keep your meetings and events organized and up to date? While the built-in iPhone calendar app is clean and functional, it's not the right calendar app for everyone. That's where the App Store comes in. There are several really great calendar replacement apps, and they can all tie into the same iOS calendar database, so all of your appointments, events, birthdays, and more will "just work". But which alternative calendar apps for iPhone are the absolute best? And more important, which one is the best choice for you?