Limited service: JFK-ORD. United operates one nonstop flight a week in each direction. Most of the time, if you want to fly between Kennedy and O'Hare, you have to make an "unnecessary" connection ... or pick a different carrier.

You don't always pay a premium for nonstops. For example, I've seen heavily discounted SEA-JFK fares that are only valid for nonstop travel; any connections would force you into a higher fare. It's a "price incentive" to persuade cost-conscious consumers to endure crappy Airbus 320 equipment instead of those nice, comfy Boeings...