How important is the CPU in a gaming PC?

So I seem to be getting conflicting information from people when it comes to the role the CPU plays in gaming PC's. Some people tell me to get the lower tier CPU, and the higher tier GPU, but others tell me that skimping on a CPU is one of the most foolish things to do. So that's why I'm coming to the pc forum, in the hopes that one of you might be able to clear this up for me.