I have a dinosaur of a computer with an AMD 500MHz CPU. The cooling fan is hella loud and probably does an inefficient job of dispersing heat. What can I do besides taking it to the dump? Suggestions would be appreciated.

I ran a K6-2 350 w/o a fan for a long time without even realizing it...but I don't recommend that.

The K6-2 500 disperses about 20.75 watts of heat.
If you got an SK-7 for $25 and a quiet fan, and undervolted the fan to 5v, the processor would be very cool, and would be dead silent. I recommend the SK-7 because it is quite possibly the cheapest all-copper heatsink that fits an 80mm fan. You could probably run the processor with the SK-7 without a fan, but unless your board has temp. monitoring, it's not a great idea.

Before you run off and do that, make sure the Socket 7 and Socket 370/A have the same clip configs. I can't remember if they do...

Socket 7/370/462 all have the same socket dimensions, but the older Socket 7 mobo's may have capacitors really close to the socket. My old Aopen AX59 pro, for example. has the end lug on each side missing 'cuz there's a cap butt up against it.

I have a k6-2 475. I bought the cheapest heatsink I could find that would take an 80mm fan (GC68, $5 or so at SVC) and a low airflow NMB fan. I had to squeeze the heatsink in next to some capacitors, but everything works fine and is much quieter. This is a more conservative route than running with no fan at all.
If yours is an Athlon 500, not a K6-2, it's a different story. I used to have one but can't remember what the fan situation was (slot processor) or whether there's anything simple or cheap you could do to make it quieter.

Any large HS designed for the current AMD CPU's will probably do, 20+ Watts of heat is not a lot. A 5v fan on a big HS probably can handle anything upto 55-60W (quietly of course). So you are in luck just check for room around your CPU and find one that fits.

Thanks for the feedback, comrades. I will definitely keep your valuable expertise in mind.