I use Digital Clock by Social & Mobile. The nice thing about this particular alarm clock app is that it is so versatile. The alarm is great as it lets you choose from ringtones or music on your phone, and the UI to set the clock is incredibly simple.

It also doubles as an exceptional bedside clock, allowing you to set it for different colors and brightnesses, has different fonts available, and is easily readable even when you're groggy in the middle of the night.

The third part of this app that works so well, is the Digital Clock Widget which looks good, works well (as far as updating and being accurate), has two different sizes (1x2 and 1x4) and a simple tap on the widget takes you right to the main app.

Having a bedside app is a must have for me, as is a reliable and accurate alarm clock, all of which this app fulfills.

Oh yeah, and it's free.

You can still find the free Klaxon around on some free sites however it's buggy on Android 1.5.

I use Alarming! which is 99c in the Android Market. It does everything Klaxon did and has a few extras as well like shake to snooze, a night clock, captcha on soonze, captcha on dismiss, ramp up volume etc.

There's a handful of other paid ones around too - all around the 99c mark.