Well firstly you need to pick a motherboard that uses the same CPU socket. If you tell us what your motherboard is now we'll be able to help you more. If you are unsure about the model you can use CPU-z.
Generally people will change motherboards without changing CPU for features. For example, more SATA connectors, different add on card slots - often more PCI-e slots or more RAM capacity / speed.
Basically motherboards will be compared by their features rather than their performance.
Do you want to use a new CPU? Then you are looking for a CPU + motherboard, and possibly new RAM, too. I'd choose the CPU first, then look for a good motherboard to put it on.
Do you want to keep your existing CPU? In that case you'll need to choose a new motherboard that supports your existing CPU - like Rusting In Peace suggested. Unless you need something like more SATA ports, or more slots, more overclocking options, then there's often little to be gained by just changing the motherboard.