The Exclusionary Rule
The exclusionary rule says that if the cops violate the U.S. Constitution to get evidence, that evidence is excluded from the trial.
Personally, I've never quite thought that was the best way to handle the situation. In my mind, the issue isn't that the accused is innocent, the problem is that the cop is guilty.
Let's look at a person who has taken someone else's things. They are, without a doubt, a thief, correct? Any time, every single time, that a cop takes evidence from your house or person without a warrant, they are thieves, and should be charged as such. I imagine that this means dismissal from their job. I understand that sometimes cops will face such a fate in order to catch a particularly heinous criminal.
The clearance rate (solve-rate) for murders in the United States is about 63%. Lots of murderers get away with it.