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As you're freely falling through the air you don't feel any force except the wind - but you're also getting *stretched* a tiny amount because gravity is a bit stronger near your feet. This is called a 'tidal force' because it creates tides: for example, water on the side of the Earth facing the Moon is pulled toward the Moon more than water on the opposite side.
As a star falls toward a black hole it can get stretched and even destroyed by this tidal force - we've seen it happen! It can create a huge flare of radiation.
But surprisingly, the bigger the black hole, the smaller the tidal force is near the event horizon. We could be falling through the event horizon of a truly enormous black hole right now, and we'd never notice - though I consider this very unlikely.
More importantly, a star like the Sun will only get disrupted *before* it crosses the event horizon if the black hole is < 100 million solar masses. Otherwise it will get sucked in and be lost to sight without any drama!
The big black hole in the center of our galaxy is only 4 million solar masses, so this 'silent death' doesn't happen here. But it happens elsewhere. The biggest black hole known is 66 *billion* solar masses!
Black holes emit flares of light that we don't understand. Some must be from stars falling in. But many flares show very little light in hydrogen's spectral lines! This talk is pretty fun, and it's all about these mysteries.
@johncarlosbaez isn't the wind resistance much stronger than the gravitational difference, and so a falling object would be compressed instead?
@clusterfcku - yes, the wind resistance vastly exceeds the tidal forces for a person falling on Earth. I hoped that was clear. But it wasn't, so I've tried to improve my statement.