Just spotted this keyword showing up on my traffic analytics for today... I guess with the game getting into the Top 10 of this year's PC Gamer Top 100, there's been a bit of a resurgence in interest in the game. This pleases me. It pleases me so much that I shall actually give you the benefit of my experience and tell you about my favourite exploits within the game.
I found these exploits by accident when I playing the game avidly in the 90's and have subsequently utilised them ruthlessly. I don't consider them cheating in the way that reloading a tactical mission if you lose one of your best soldiers is cheating - I think of them more as "game features". Bugs, in other words.
The first exploit is by far the most useful in the early game. If you transfer an Interceptor (or other aircraft) from one base to another and sortie it immediately after it arrives at the base, it will be airborne with 0% fuel. In effect, it will never run out of fuel (because it had none to begin with) so you can keep it in the air on a combat patrol indefinitely - or at least until it runs out of ammunition. This makes it a good strategy to research Plasma Cannons as quickly as possible, because then you can keep your Interceptors in the air continuously, which is great if you're having a problem with an area that's not near one of your bases. Just remember to put them back on patrol once you've shot down a UFO so that they don't return to base and refuel.
The next exploit is useful throughout the whole game. On the tactical map, you can use the selection cursor to explore the dark areas of the map to give you a clue of where the aliens might be. The cursor will be occulted by objects on the map, so it's particularly good for finding out which building an unseen alien is in by running the cursor along the lines of the internal walls if you hear a door opening. It's also quite handy to check whether the power sources of UFOs are intact or not, so you're not overly judicious with the use of a Blaster Launcher, for example...
But by far the best exploit in the entire game is The Great Intra-Base Personnel Transfer Swindle. You only get charged the salaries of your soldiers, engineers and scientists at midnight on the 1st of every month. So if they happen to be in transit from one base to another as the month turns and you get the end of month report, you don't pay their salaries... This also works with aircraft as well, but that's not quite as useful, as you don't want craft to be out of use for a day or more as they're transferred. But it's great for engineers and scientists. As long as you leave a solitary scientist or engineer on the project they are working on, you don't lose any of your progress. So I used to have three or four separate research teams of at least 100 scientists of each, and I'd only end up paying a single scientist's salary at each base with laboratories, since I'd put all the rest onto planes at 23:00 on the last day of each month and send them off to another base. The transfer costs are a fraction of the salary cost, so you can literally save millions of dollars a month. Having 500 scientists but only paying for 4 or 5 each month means that you whittle your way through the research tree pretty darned quickly without bankrupting yourself. A very handy strategy in the middle to end game where your expenses would otherwise dwarf your income.