Going through stuff to throw out, and came across old games like X-wing, Doom, Quake, Front Page Sports stuff, etc.. Is there a site on the net that will buy these older games, or should I just toss them out?

You can try dumping them on eBay or Amazon Marketplace first.

There's a trading/selling forum on this very site too.

You are throwing out X-wing!!! For older PC games, you may not be able to get much money for them. Of course, if you have the game with their original box and manual, then you will undoubtedly get more money, depending on the game and condition. Unfortunately, I don't think that PC sports games will get you much money, but it doesn't hurt to try. Also, you could give away the games that you can't sell. Doing this helps to fund thrift stores and libraries, as opposed to contributing to a landfill.

Adventure games will probably fetch the highest amount of money, especially if they are out of print and desired. Action and FPS games might fetch you a dollar or two, and sports games might only yield something like .25 cents. As always, it depends on the title of course.

Or you could keep them an get yourself an nice DOS emulator like DosBox.

I have a bunch of old stuff that I'd hate to just throw away. If I ever get organized enough to be able to find and list them, I'll offer them up here. Probably won't bother with ebay for just a hundred bucks or less.