They do and they don't. The answer is kind of murky. If you have a motherboard with a PCIe x16 slot, that will affect performance over say a board with only an x8 slot. However, if you have two boards with more or less equivalent specs, then they should have equivalent performance.
The chipsets tend to be what determines certain features offered on the board. XYZ chipset may not support PCIe 3.0, but chipset ZYX does.
I should add that Intel has a new CPU, code-named "HASWELL" (probably an i5 and i7 4000 series) which is coming around JUNE or so.
If you can wait to build your computer, I strongly suggest you do so. If naming conventions continue, the following MIGHT be the next recommended gaming CPU at about $240:
The reason I recommend waiting is that Haswell can massively reduce power consumption (mostly in idle). It's not just a 10% improvement, apparently it's supposed to be a huge difference because the CPU can rapidly turn off and on constantly thus managing OFF states while the computer is "running".