Choosing lights for my bike
The main things to look for when purchasing new lights:


How bright are the lights? Can you see them for a few feet, a block, half a mile, etc?
What is the angle of visibility of the light? It does you no good if you can only see the light from one single point - you want to be sure your light can be seen from a wide range of angles, especially for your rear light.
What features are included? - Do you get multiple levels of brightness (for your front light) or different flashing modes (for your rear)? It's nice to have different flashing modes on your rear because it catches people's attention at lot quicker than a steady light.
How long do the lights' batteries last? You don't want to get caught out with a dead battery (trust me, it's not fun)
To go along with the above - rechargeable set or normal batteries? The rechargeable is a lot nicer IMO, because you don't have to worry about getting AA/AAAs every few weeks/months. However, it's a lot harder to bring or find backups if you're going to be out for quite a long time. If you go with AA/AAA's you can also use rechargeable versions, which would cut down on the cost if you use your lights often. 
Price point - How much is your safety worth?
Theft/secturity - How often do you need to worry locking your bike up in an area where people can take / mess with your equipment? If it is quite often, you'll want to look into something that has a quick release from the light to the frame or rubber O-rings (those are fairly easy to take on/off often) - thanks Colin Newell