For instance, aftermarket remote-starting systems are a disaster for the intertwined computer systems of new vehicles, where every component talks to every other component on a constant basis. (We make pretty nice coin uninstalling these things, coincidentally.) Of course, if you don't mind driving around with three or four warning / indicator lamps glowing in your dash, then go ahead and slap a remote-start system in your new car.
Same goes for aftermarket stereo systems, though in my experience, these have a lesser incidence of inducing problems. In the newest vehicles, the factory stereo (especially in Cadillacs, for instance) is probably a major communications hub for all of the vehicle's computer-controlled data traffic. Take that bridge out, and you gots big traffic problems.
Yes, aftermarket supra-bright radioactive halogen fog lamps look cool. Except for the fact that they're pretty much lethal to factory wiring harnesses. Any factory wiring near the lamps will be dark, crispy, and inoperative in no time.
Extra-wide aftermarket tires and wheels may look sweet. But they will likely kill whatever decent ride your SUV might have had to this point. They will also probably rub your inner fender wells incessantly when you make even the widest turns, shredding the sides of said tires into oblivion. Throw in the fact that they're usually noisy as heck on the highway, and you have a big, big winner.
Yes, lowering your vehicle will void any manufacturer's warranty on your suspension and undercarriage system. (No, what the aftermarket installation shop's head guy told you does not matter.)
I'm probably forgetting other things, but hopefully you get the idea!