Cheap or poorly built wheels will break spokes. And cheap spokes break more easily. Good quality wheels, especially hand built ones are expensive. Machine built wheels can be hit or miss. I recently re-tensioned all the spokes on a wheel on a $1500 bike. It was only a year old, but the spoke tension was so unbalanced that some of the spokes were completely slack, and none had enough tension. If the tension is too low, spokes are more likely to break because the stress changes more as the wheel rolls. Too much tension will break spokes, too, but that's usually not a problem. I have one mountain bike with machine built wheels (I'm assuming-- most factory wheels are), and they haven't needed even the slightest adjustment over the life of the bike (a few years). I have one high-end hand built wheel on another bike, and again it has needed no adjustment in a year. Number of spokes doesn't necessarily matter, because my cheap commuter with 36 spokes breaks one every so often.
When looking at wheels, especially on a used bike, there are a few things you can check:
-Is the wheel true? Rest your finger on the frame near the rim and spin the wheel slowly. If the rim gets closer or farther from your finger in some spots, that can be a bad sign. It might just need to be trued, which a bike shop can do for $10-20, or it might be bent in which case there is almost nothing that can be done by adjusting the spoke tension.
-Is the hub centered, radially? As you spin the wheel, look for any areas where the rim looks like it's going up and down. The tire might do that a little, which is OK, but it should be minimal on the rim.
-Are there any flatter spots on the rim? The curvature should be the same all the way around. Also look for dents on the side and where the bead hooks in. Any cracks would also be bad.
-Is the wheel roughly centered in the frame (dished correctly, and the frame is straight)? If not, that could indicate a bad wheel build or bent frame.
-Is the spoke tension roughly even all the way around? Each spoke should make a musical sound when plucked or tapped with your fingernail. The tone should be very roughly the same all the way around. If one is very low or sounds dull, it might not have enough tension. You can also estimate by squeezing pairs of spokes together to see how much force it takes to bend them. On the rear, one side will have more tension than the other, but both sides of the front should be about the same.
Practice this 3 minute bike inspection and do it whenever you go look at a bike on Craigslist. It will take more than 3 minutes, and it's more thorough than most people will ever be.
http://www.pinkbike.com/news/Tech-Tuesday-Three-Minute-Bike-Preflight.htmlWhen buying a bike, you will get a good deal if you find someone with a bike that has something wrong with, and you know is easy to fix but they don't know how to fix it (minor adjustments, small parts need replacing, cosmetic defects, etc). It's a bad deal if you get a bike with something that's difficult/expensive to fix, like a cracked frame, bad wheels, bad fork, badly worn drivetrain, etc.