I'll add Death Rally to the list. A top-down racing game with weapon pickups along the race track, and you earn money for races that you can use to upgrade your car or buy a better one, and pay to have some dirty tricks done to your opponents that'll leave them at the starting line, etc etc.
The Settler series, first 2 parts were on DOS before moving to Windows with 3rd installation. Basically a mash between Age of Empires and a logistics simulator, you have to expand your borders and fight other empires while securing a steady supply of resources to make sure you can be succesful. Need a bigger army? Soldiers need equipment, so you need to have a source of iron and coal for the smelter to turn ore into ingots, which you will then have to supply to the weaponsmith. Soldiers also need to be paid, so a source of gold and a mint to make coins are essential. Miners cannot provide these on an empty stomach, so you better supply them with a versatile diet - bread alone ain't gonna do it, so you need pig farms and a slaughterhouse, and a few fishermen are good to have too. Hunters are fine too in case you're not ok with raising animals for meat, but they're not as reliable. All these professionals need tools to work their jobs, too. Wood and stone needed for construction jobs isn't going to magically appear either. Efficient routes for mentioned materials to travel on make everything easier, so plan ahead.
Pizza Tycoon is awesome if you like pizza and in-depth micromanaging. You start in a city of your choice as a newcomer pizza entrepreneur. You need to purchase a place to run your business in, get it up and running, open new pizza joints, and eventually go global and put your competitors out of business. EVERYTHING matters in this game, from location and demographic makeup in the area to the style and quality of your interior decoration and quality of ingredients you use for your pizzas. Senior citizens are into expensive and stylish interiors, but don't like their pizzas overly sweet or spicy hot, so if there're a lot of these people in the area around your restaurant, you better adjust the menu accordingly. Opposite goes for kids and young adults. Your staff needs to be reliable and well-trained, and your pizza oven capacity much match the size of your restaurant. There are multiple vendors to purchase ingredients and furniture from, and the quality of purchases affects customer satisfaction. Quality comes with a price, though! If competition is too hard, you can resort to dirty tricks and attack your competitors restaurant with a flamethrower or spice up their pizza cheese with a healthy dose of laxatives, among other options. But beware, messing with the underground means some nasty-looking characters might appear in your restaurant and demand protection money. You either pay them or you'll find yourself shopping for new furniture soon!
Edit: the game's strongest point (for me at least) is the fact that you build your pizzas yourself, by hand. You start with an empty pizza bottom and slap ingredients on that. This is also the basis for the game's innovative copy protection, which means that you must have at least 3 basic pizzas on your menu, put together exactly like in the game manual, or your restaurant won't have any customers coming in. AFAIK gog.com version does not include the manual with the download, but it's easily found online.
Sid Meier's Covert Action is a game of yesteryear that I most often find myself getting back to nowadays. Insanely ahead of its time, in Covert Action you roleplay as CIA agent and try undo the plans of global criminals/terrorists. Each case you need to solve is randomly generated from premade coarse plot lines, and you're given some small clues at the start of a case that you need to follow in order to uncover more and get an idea what's going on. Actual gameplay consists of series of minigames including espionage, wire tapping, decyphering coded messages, car chases and tailing suspects, and so on. Suspicious traffic at a certain safehouse? Break in to photograph file cabinets and safes for evidence, place listening devices, arrest known suspects if you have strong evidence against them, and while doing all this you must remain hidden as the building is full of guards. Suspect A sent a coded message to suspect B? Get your brain working, and figure out which letters are replacing which and find words that are repeated often to decipher the code and obtain valuable information regarding the terrorist's plot.
Not exclusively a DOS game, but I recommend trying out the original Fallout, which I prefer over what the franchise has become after Fallout 2. More compact and enjoyable package, if you can deal with the game engine that hasn't aged well.
The first Carmageddon is worth getting to know, IMHO. Though I can't play it because the low resolution and heavily pixelated graphics give me a serious headache nowadays.
I'm glad people mentioned Build engine shooters like Blood and Duke Nukem 3D, and if you like those you should really check out the following titles:
Outlaws, a western-style shooter about a man with nothing to lose.
Redneck Rampage. Rednecks shooting aliens. Like a classic, campy B-movie from the 80's.
Shadow Warrior, the equally macho and politically incorrect oriental-ish version of Duke Nukem. If you liked the 2013 reboot, you're gonna love the original.
I'll edit this post later to include more stuff. These I could remember now on the top of my head.
