Pieces

Back in 1942, a little boy killed his mother with an axe and then used a chainsaw to cut off her head because she got really, really mad at him for putting together a jigsaw puzzle of a naked lady.
Now it's 1982 and the female students at a generic university are being horribly chainsaw murdered. Clearly there's a connection.
The police are baffled but the audience is clearly supposed to think the killer is either the squinty gardener or the mustachioed anthropology professor. They enlist the help of the boyfriend of one of the victims (who should probably be a suspect but clearly he isn't because he looks kind of like Mark Lynn Baker) and the police department's resident tennis star (every precinct has one) to try and find the killer.
Pieces is hilarious. The dubbing and dialogue are awkward, the kill scenes are fun, there's a random kung fu guy for no good reason, the forty year old blood on the murdered mom's clothes is still bright red and it's just an all around entertaining movie. I'm surprised it's not more popular.
My favorite scene involves the killer going after a girl in a swimming pool. He catches her head in a net that she could easily duck under and swim away from, but instead she grabs onto the side of the net, mildly complains that she can't breathe and lets him drag her out of the water. Then, rather than attempt to make an escape while he leaves her by the pool to get his chainsaw, she stays by the pool and patiently waits. It's comedy gold, I tell you!
Great. I just gave away the funniest scene in the movie. Sorry, guys. Don't worry, though, that happens fairly early on and it's still worth seeing.
And, if you would like a more in-depth and well-researched review, check out what Justin Case has to say on the subject.

End of line.
-Sally