@ philcore
It depends on what you call "stopping power". Hollowpoints perform very well against unarmored targets, but what if the bad guy has a vest or many layers of clothes? I want the penetration of full metal jacket. I'd rather take my chances with overpenetration than take my chances with no penetration. Also, I carry an M1911-derived pistol (Colt's Mfg Mark IV/Series 70 to be exact) in .45 ACP, and .45 ACP FMJ will stop anything on two legs in one round no matter what. My rifle is a modernized/custom USGI M14, and it's the same story. 7.62x51mm NATO FMJ will stop anything on two legs no matter what. Basically, the advantage of hollowpoint does not outweigh its disadvantages considering the types of firearms I own, and as stated above I disagree with their use in principle. They were banned from warfare for a very good reason.
@ Draugnar
"But it also has better penetration than traditional rounds, which is why police use it."
Nah, police use 'em because there's much less risk of over-penetration, which is the only advantage of hollowpoint in my book. Also, police generally (and stupidly) use 9mm pistols, so they need to use hollowpoints to squeeze a little more stopping power out of that round. However, I'd rather take my chances with over-penetration than under-penetration. I don't know if the bad guy has a vest or not, but I'm erring on the side of my safety. Also, as mentioned above, .45 ACP can stop anything no matter what load I use.
@ philcore
"Oh, I think those are the bullets with the X carved in the top. They call them cop killers, I believe and they are illegal."
Bullets with an X carved on top are hollowpoints, or bullets that are designed to expand. They are completely legal for civilian use in the United States and they are not widely considered to be specialist ammunition. Many private citizens and police officers use it for its increased stopping power against unarmored targets and its reduced risk of over-penetration.
It is NOT referred to as a "cop-killer" round. In fact, most hollowpoints would be easily stopped by police body armor. The alleged "cop-killer" round is the 5.7mm pistol round developed by FN for their newish Five-SeveN pistol and P90 PDW. The 5.7mm is basically a miniature rifle round and is specifically designed to penetrate body armor, even better than conventional FMJ pistol rounds. This round and that pistol are not illegal in the United States at present, but the wackos at the Brady Campaign are trying to get them banned (they coined the false "cop-killer" phrase)