We use a lot of rechargeable batteries at home, and I can never tell which ones work and which ones need to be recharged, and finding out is a pain because very few things run on just one battery, etc, etc.
So, I made something to test single batteries. It's crude and it's ugly, but it does exactly what I want it to, it works, and it cost me almost nothing. This one just does AAs, simply because I only had a single AA battery holder on hand and I mainly use those anyway. It can easily be adapted for different kinds of batteries, or more than one at once.
Here's how it works: You put a battery into a little battery clip, and if it works, an LED lights up. For that reason, it's going into the LED contest (*crosses fingers*).
(I made this without thinking to photograph it, so I'll recreate it with some diagrams and new photos.)

Step 1: Materials

1 LED (any color)
1 NPN Transistor
1 Old AC adapter (preferably a lower voltage than the one I used)
Resistors in accordance with the voltage and current of your adapter (I used 2x 180Ω)
1 single AA batter holder (or other kinds, or more than one kind, just single battery holders)
A container of some sort (I used a flowerpot and some rubber rings)

Step 2: The Circuit

Because 1.5V is not enough to power an LED on its own, the whole circuit runs off of an old charger (AC adapter). The one I used provides 12V at 1A, which is a little high for this application, but it's all I had.

Step 3: Set Up and Solder

You may want to set up the circuit on a solderless breadboard first to test it. Solder all the parts together, insulating with heat-shrink tubing. Use this diagram and the schematic for help