The short of it is you should look at the 12 volt category to see if it meets your needs. If 12 volts isn't powerful enough, then look to the 18 volt category unless you're sure you want the in between 14.4 volt size.
12 Volt Cordless Drill
The 12 volt drill is small and lightweight. I recommend this category to most "home-use" buyers. 10 years ago this category may have left you wanting more power. But with the advent of li-ion batteries, good 12 volt drills are capable of doing just about everything around the house. Check out this review of the Milwaukee M12 drill to see what you can expect from a good 12 volt drill. The advantages of going with a smaller drill are lower price, easier to handle, and fitting in smaller places. Check out our 12 volt recommendation here.
14.4 Volt Cordless Drill
The 14.4 volt category is in between 12 volts and 18 volts. That's obvious, of course, if you think of 12, 14.4, and 18 volts as small, medium, large. The problem is that 12v drills fill the role of 14.4v drills now. And while newer 14.4v drills can do the work of older 18v drills that was never the point of an 18v cordless. The point of an 18 volt cordless is that it's the right size for most people. And people want as much power and battery as they can get in that size package. So the 14.4 volt drill never overtook the 18 volt. There's still a place for this category if you want something smaller than an 18 volt and more powerful than a 12 volt. Medium. Check out our 14.4 volt recommendation here.
18 Volt Cordless Drill
The 18 volt cordless category is the flagship for most manufacturers. There's just something about this size and weight that appeals to a lot of people. It's big enough to pack a punch, but not so big it's uncomfortable to use or hard to maneuver. Many professionals are comfortable using this size drill all day long. For these reasons 18 volt drills have a historical importance as well. Many cordless drill buyers first thought is that they need an 18 volt drill. Manufacturers devote more resources to their 18 volt drills. So the 18 volt category is a good place to be for power and endurance is a reasonable size. Check out our 18 volt recommendation here.
24 Volt Cordless Drill
The obvious reason to move up from the 18 volt cordless category to the 24 volt category is to handle applications an 18 volt drill cannot like large lag screws (with pilot holes), drilling through brick/concrete, etc. I should note if you just want high torque for driving you should look into an impact driver (NOTE: impact drivers are good for driving but not for drilling. See this article.) The down side is that 24 volt drills tend to be too bulky for extended use. Maybe you're man enough to use one all of the time, but most people who need a 24 volt cordless will use it as a second drill for heavy duty applications. Check out our 24 volt recommendation here.
36 Volt Cordless Drill
The 36 volt category is hard to classify. For example, Bosch has two entries in the 36v realm. One is a beefed up 18 volt drill with more torque and more battery. The other is a 10 pound monster with a true hammer function (like for busting up concrete). While both are 36 volt drills, they are vastly different. But either way, the reason to consider a 36v cordless is to get the most power you can get in a cordless. Check out our 36 volt recommendation(s) here.