Death Rally is a game that is quintessential nostalgia to me. I remember going over to my cousin's one time and there it was. I had played racing games before, sure, but not with guns and stuff.
You can play it like any other racing game, but that's not what you paid for. It's not a cute one like Mario Cart either (thank goodness!). A variety of cars can be loaded with guns, mines, spiked bumpers, even rockets!
You start off with a car that looks like a Volkswagen Beetle, then as you make money from winning races, you upgrade your stuff (tires, engine, armor), and eventually the car itself. The next is a pickup truck, then a variety of unassuming cars, and ending up with some kind of futuristic space chariot (as shown).
If you care to read the descriptions and comments of stuff in the shop, there is a definite underlying sense of humor to the game. Whoever wrote it must have seriously lived, breathed, and loved the race. Stuff like "Zorro's Zs were nothing. Carve your whole signature", "Got your wax coat scratched? Want to be your shining best? Hey, whatever lights up your dashboard," and "If speeding is the 8th deadly sin, with this babe under your hood, you are now past redemption." There is also a hint of a backstory of someone named True Tom Rhymer, who went against The Adversary, and lost.
Each race is only a couple of minutes (for me at least). There are three levels of race (easy, medium, hard). That choice dictates what other cars you will face, so you want to have a better car (and possibly more upgrades) to compete in the more difficult races. Not coming in last earns you cash and points in the ranking. Use the cash to repair and upgrade. Having the best car and running the easy races might not bring in enough money to cover repairs. Once you reach the top of the rankings, it's your turn to race The Adversary, who has an even more souped up car.
It came out in 1996, I bought the thing on CDROM (so 90s!) about 7 years ago or so. I figured out how to run it really well in DosBox. (Leave a message if you want the config file.) It went free to play about two years ago, and an ipad port came out several months ago. Now I hear there is a re-release on PC next month. I'll certainly be checking it out. There's also a series of some bizarre trailers for the re-release on YouTube.