Recently I got a new motherboard and was installing it into my computer when I realized that while my CPU heat sink had screws, the mobo holes didn't have screw holes, but instead simply had holes meant for pins. My question is, should I buy a new heat sink or try to drill holes in the mobo and hang the heat sink on the new holes? Thanks in advance.

New motherboard always deserves a new heat sink and a quality fan. You should never have to consider doing anything to your motherboard which would void the warranty. A combo pgk of heatsink and fan, with thermal past, should cost you $12 to $25 depending on size, brand, and quality.

Drilling holes into your motherboard rarely turns out good.

Just buy a new heatsink/fan - what CPU are you using, and are you overclocking?

motherboard:GIGABYTE GA-8I945GZME-RH LGA 775 Intel 945GZ Micro ATX Intel Motherboard
CPU: Pentium4 630 (P) HT 3.0 GHz:

can you guys help recommend some coolers to me? Thanks.

Look for a HSF (Heat-Sink, Fan) suitable for a Socket LGA 775 type CPU

I use this sweet HSF:

http://www.newegg.com/Product/Product.asp?Item=N82E16835118003

There are cheaper HFS's out there

Cooler Master, ThermalTake, Scythe Ninja, Spire Verticool II.
I like the simplicity and the long fan life of the Cooler Master, unless you are ready to take the plunge into water cooled coolers.