Tough to top what Bob said, he gave excellent info and examples.
I only just recently learned that some APS-C sensors were a crop factor of 1.5. I’d always heard of them as being 1.6 crop factor, and that’s how I still think of them. Maybe brand does have something to do with it.
I really prefer to think in “full frame” terms. My last two cameras have been full frame, and I really can’t see going back to a crop body. But like Bob said, that’s just the style of photos I like to take. My sister uses a crop body (Canon 7D), and it’s perfect for her. She loves wildlife and moving subjects, and her 70-200mm lens really gives her a lot of bang for the buck on a crop body.
Funny enough, I absolutely loved the exact same lens on my full frame because on a 35mm equivalent, 70-200 is a really nice and useful range. In fact it was my primary walk around lens.
I’m by no means an expert, just an enthusiast, but I’m currently at the point in my photography where I let the lens quality dictate my purchasing choice, not the focal length. I want the best glass I can afford in my price range, and I’ll work around any limitations in focal length. This is also the reason I’m switching to primes (although truth be told, the 70-200 f/4 L IS is a phenomenal zoom).
One bonus to consider about full frame sensors, especially on the newer cameras, is they often remove the need for a zoom. The resolution is so incredible, even at 100% crop, that you can get very usable photos simply by cropping a wide angle shot.
This is just an example…although these are obviously two different photos, they were taken from the exact same distance, and show you just what kind of cropping you can do with a full frame:


…See, who needs a zoom lens? Hahaha ;-)