Painting is variable. Usually you get better over time. What happens, then, when you look at old models and say "that's not good enough anymore"? Or, what happens if you buy some bitz or models off of ebay that were painted by a blind idiot with a toothbrush? You need to get rid of that paint.
Stripping models is important for any model gamer. There are several methods, some of which work better than others.
The first models I stripped used a high pH liquid soap called Super Clean. This was incredibly inconvenient, and only worked after repeated soakings and scrubbings. The next thing I tried was pure toluene. It worked fine, but only for pewter minis. It ATE a plastic base I threw in by accident. Plus you need to do it outside as toluene has awful fumes. For a while I tried Isopropyl Alcohol. This worked almost as well as Super Clean, and with less hassle but more scrubbing.
Then I was stripping some Necromunda gangers I bought at Gen Con. I used undilluted Pine Sol. The painte FELL off the minis when I barely touched them. It was the greatest success I've had stripping. Lexington said he tried Pine Sol on plastics and it lost a little bit of detail when soaked overnight, but it stripped the old pewter Land Speeder he's had for decades.
For a final verdict, I choose Pine Sol. If I need to strip plastic, I'l try diluting it 50/50 with water and scrubbing after a few hours rather than letting it soak all night. But on metals it works WONDERS.