What can I do with a bunch of old 1GB/512MB DDR2 RAM sticks?

Well... for a desktop, you could purchase a Gigabyte iRam which turns 4 1gb DDR sticks into a 4gb drive. Yes, that's not all that much space, but it is an extremely fast drive. There weren't many (any?) consumer grade motherboards that would utilize a ton of DDR or even DDR2 Ram. You'd only find that in server grade equipment. As far as laptops go, only high end custom equipment would support more than 2 sticks of Ram. Clevo/Sager made units that would use 4 or even 8 sticks of SODIMM Ram... but as has been pointed out, the cost of purchasing equipment just to use the Ram would outweigh any benefits.

For the Newer DDR2, you could use something like the Acard which supports up to 8 sticks of DDR2 (64gb total) and turns it into an SSD.

They make nice keychains, until the chips start falling off.

besides eBay/craigslist/giving them away, what good things are there that can I do with all of this RAM?

They are worthless to any computer that requires DDR3 which has been standard for about 7 years now. There only worth would be to somebody who uses a computer that uses that standard.

If there was some computer out there with a whole ton slots for consumer (non-ECC) RAM (especially laptop RAM), I could make it pretty powerful, memory wise, using only spare parts.

You would have to purchase a motherboard and CPU that supports this memory. If you can find that hardware it likely would cost you 2-3x the cost of current hardware. The memory limits were around 2-4GB at the time DDR2 was used. The kind of hardware you could build most likely would not be worth the money you would put into building it.

I guess I could make some low-memory dedicated home servers or small-form-factor machines, but I already have a home server and don't really need too man more computers lying around.

Sounds like you have no use for this equipment.