I heard somewhere that the Intel Core 2 Duo is backwards compatible with boards that use plain old Core Duo CPUs. Is this true? I have a laptop I want to upgrade eventually to either a Core 2 Duo or a Core 2 Quad.

The slot on the motherboard to plug in a CPU is called the socket. If you search a bit, will you find on this page:
http://en.wikipedia.org/wiki/Core_duo

If I'm not mistaken, Core Duo was only released for laptop.

The Core Duo used Socket M, while the Core 2 Duo (E4,6,7,8xxx) use Socket 775, which is not the same, hence not compatible. On a laptop though, Core 2 Duo do exist with Socket M (Mobile Core 2 Duo T5xxx and T7xxx). I never had any experience about upgrading a laptop processor though, might get complex.

Imho, this is one of those questions that if you have to ask it, you shouldn't attempt at doing it.

I'm not trying to be rude here, but laptops are not "plug and play" upgradeable like regular desktop pc's. If you have the skills and tools to upgrade a laptop, then you'd know the answer to your question (or how to easily find it).