There are many 775 socket boards that support ddr3 and core 2 duo/quad supported ddr2 and 3.

There are even motherboard that support both ddr2 and ddr3 like this gigabyte g41m combo

Edit: damn at least some core 2 duo’s support also ddr1. So core duo supports ddr1, 2 and 3

There are almost no lga 775 boards that have ddr1 support and have core 2 duo as supported cpu. But this ASRock motherboard does support the core 2 duo and ddr1 and ddr2