Android - Is there an app that will drain my battery?

Do not do this. You are actually harming the lifespan of your battery when fully discharging it before a recharge. See this site for a discussion of how depth of discharge affects battery life.

The only reason you might want to fully discharge before a recharge is if you have a NiCad battery that is susceptible to the memory effect. Your smartphone most likely uses a Lithium-ion polymer battery, so there is no good reason for you to totally discharge your battery. The lifetime is longer if you have a shallow depth of discharge.

This question is along these same lines: What causes battery to drain faster than it can charge?

So there may or may not be an app designed to drain the battery but you probably just need to turn on an app that uses the GPS. This will help to fully drain your battery but I don't know that doing so before recharging will extend the battery life.

I know that my phone -- HTC's Evo -- actually has a diagnostic tool thats sole purpose is to drain the battery as fast as possible. Open up your dialer and enter:

*#*#3424#*#*

You don't need to press send or anything. A recent update for the Evo blocked these tools so hopefully you can still access them. You can also look up device specific codes if yours happens to be different. Rooted users have found a way to get these tools back.

The utility turns up brightness all the way, prevents sleep, turns on the camera and flash, turns on the GPS and constantly polls it, etc. Basically everything that can drain the battery but not damage the phone is done (ie it doesn't constantly vibrate because that would probably be bad).