You can either build something a large number of people want a small amount, or something a small number of people want a large amount. Choose the latter. Think of companies as holes: dig a well (narrow and deep) rather than a crater (broad and shallow). Microsoft's Altair Basic and Facebook at Harvard both started as wells.
The 'well' framework for evaluating demand
The danger of a made-up 'sitcom' idea is that when you run it by friends, they say 'Yeah, maybe I could see using something like that' instead of 'I would never use this.' Sum that lukewarm reaction across a population and you get zero users. The set of plausible-sounding startup ideas is many times larger than the set of good ones.
Ask yourself: who wants this so much that they'll use it even when it's a crappy version one made by a two-person startup they've never heard of? If you can't answer that, the idea is probably bad.
Successful ideas are the result of some external stimulus hitting a prepared mind. Gates heard about the Altair; Drew Houston forgot his USB stick. Lots of people heard the same things — what mattered was preparation to notice the opportunity.
Working on things that could be dismissed as 'toys' often produces good ones. When something is described as a toy, it has everything an idea needs except being important. Microcomputers, BackRub, and TheFacebook were all initially dismissed this way — at YC, hearing know-it-alls call something a toy is positive evidence.
Turn off the schlep filter and the unsexy filter. Stripe succeeded because thousands of programmers knew payments were painful, but they unconsciously shrank from dealing with them. Any sufficiently good idea will have as many schleps as one you're avoiding — so don't dodge them.
You don't need to worry about a 'crowded market' so long as you have a precise thesis about what everyone else is overlooking. Best of all is when you can say incumbents didn't have the courage of their own convictions — early search engines shied away from the fact that the better job they did, the faster users would leave.
The clash of domains is a particularly fruitful source of ideas. A CS major looking for startup ideas is better off taking a class on genetics — or getting a summer job in an unrelated field — than taking a class on entrepreneurship. You see problems software could solve precisely because you don't yet take the new domain's status quo for granted.