Some of these depend on game settings.
Add your own below, or correct me if I've got any wrong.
You can Control-click on an object to drop it from the inventory screen.
You can Control-click when moving to sprint.
You can Control-click when firing to try to shoot through walls.
You can hold down Alt to reveal the location of enemies your characters have spotted if that part of the map isn't revealed.
Grenades won't explode in your hand if the time runs out.
You can throw things further indoors if you're crouching.
Enemies have all their time-units reserved for reaction fire on the first turn of battle, making popping your head out dangerous. Wait, or use lots of smoke (not that I ever did) or send an expendable scout out first to draw their fire.
Reaction fire only works via snap shot attacks - auto-fire-only weapons are useless.
If you fire even a single bullet, you will always lose the entire clip after a battle, unless Statistical Bullet Saving is enabled in the menu.
Some creatures are near-immune, or completely immune, to Stun damage - though you can still capture them in other ways (like if you have a weapon which inflicts another type of damage plus bonus stun damage).
'Invisibility' just means you can only see the target on the diagonal.
Make sure you have some explosive weapons for tough enemies - someone on the roof of your ship with a Mortar can destroy tanks from long range without even needing to see them.
Doubling the number of Brainers on a research project doesn't double the speed - it's more efficient to split them up across multiple projects.
Early research projects with unpromising names like 'Flintlocks & Bombs' are essential pre-requisites - these are more important than, say, researching the same type of prisoner multiple times.
'Superhero' allies may not seem very good, but they're worth testing to destruction.
You can't have too many Damaged Grav Units or Power Armor Parts. If you can get those by robbing a prisoner, that's more useful than ransoming them. On the other hand, plasma weapons take such a long time to learn to use, you can just sell off the ones you find early on; there will be plenty more later.
Make sure you understand the difference between the vessel weapon slots. Early on, the Seagull launcher is available, but horribly expensive. Heavy weapons are generally pretty great, but most fast interceptors can't use them.
The minimize button in the top left of the ship-to-ship combat window causes time to continue passing, allowing you to attack a single foe with up to four ships.
Just because you shoot down a ship, it doesn't mean you have to assault it. There's no shortage of potential targets, and you get better loot attacking intact ships that have landed on their own.
