If your favorite part of cable is watching movies, cutting the cord might just maximize your bliss. Much like cable on-demand services, you can rent many of the latest releases on iTunes or Amazon for about $5 apiece. HBO also carries a wide selection of recent movies, and Netflix has a large back catalogue of films (though titles will appear and disappear somewhat randomly).
You probably want amplification, unless you're living next door to the local broadcast tower. They don't make the signal stronger coming in the house; they make an already low signal strong enough for the TV tuner to use. Even some of the flat antennas have amplification options; but amplification ups the cost. Setup is easy, but you'll have to play with the antenna position to maximize reception—just like fiddling with rabbit ear antennas in the 1970s. Some outdoor antennas can work from inside if they're up high—say in your attic—if there isn't a lot of obstruction.

The question of "when does it make sense?" can easily be rephrased as "how much money can I save?" and one of the biggest factors will be the price difference between combined internet and TV service or just internet. These are also the options that vary the most widely based on where you live, and the availability of promotions or contracts that can keep prices down for a short time.