It isn't the most original idea, but if you have enough parts to build a new machine—with or without a good case—you can always throw it together and re purpose it like you would an old computer. For example, no matter how old or crappy a computer may be, it can make for a pretty great home server that feeds files to the other computers in your house, downloads torrents 24/7, or performs other all-day tasks. It also doesn't take a lot of power to build a home theater PC for all your movies and TV shows, so that's a good option as well.
*Note that if you don't have an old case to use (since cases can pretty much last forever), you can always make a temporary case out of a cardboard box, or build that computer right into your desk or entertainment center for true household integration....
Some parts can be repurposed on their own. For example, you can easily turn an old hard drive into an external hard drive with a simple enclosure, or turn a DVD drive into an external DVD drive. If you have some extra NVIDIA graphics cards, you can throw one in your existing computer as a dedicated PhysX card for games that support it (and if your current card isn't too powerful). If you've really got some DIY skills, you could even turn it into an external graphics card for better gaming on your laptop. Not all parts can be repurposed this way, but before you start throwing stuff out, see if any of them have use to your current computers.
This one may not be particularly useful, but if you have a lot of parts lying around and want something fun to do, you could always turn them into a fun computer-themed DIY project. For example, you could turn an old PC case into an aquarium, turn old motherboards and graphics cards into a circuit board coffee table, or one of a million other cool things. Search around to find projects that others have come up with, or think of other ways you can decorate your geek cave on your own.
You may not have use for an old Intel Pentium 4 and an AGP graphics card, but someone else might. If you can't think of anything to do with them at home, put them up on Craigslist or eBay and see if you can make a few bucks. You can either put them up as single parts or build them into a few computers and sell them that way. You may not get a ton for your efforts, but you'll at least get some extra pocket money, and someone else will get the parts they want. Just make sure you don't get screwed while selling online.
If all else fails and you just want to get rid of those old parts, don't throw them in the trash. Those parts could have harmful metals in them you don't want rotting away in a landfill. We've run down five easy places to recycle your old computers and computer parts, and those suggestions should still hold true. Your individual city may have other options and locations, too, so Google around—you should be able to find an easy, free place to get rid of those parts in a responsible way.