Exploits
Throw through ceilings
Most explosives (grenades, HE packs) can be chucked up through ceilings to land on the floor above. This is useful if you don't know where enemies are exactly, but you know where they are roughly. Use a big enough boomstick (HE rounds, pointed at ceiling) and you'll probably kill anyone in the vicinity of the blast.
Corner Tile Tricks
Diagonal exterior UFO tiles aren't a well-defined boundary. A grenade thrown onto the same square from outside will detonate inside the UFO. An unconscious volunteer thrown onto the same square from outside will awake inside the UFO. (Except if he's sharing the tile with a live grenade.) A Flying Suit can sometimes fly up into a UFO from beneath a diagonal overhang.
Infinite Fuel.
This trick is great for saving Elerium-115. When you finish building a new ship, load it out with weapons (dual Plasma Cannons are recommended) and wait for it to have the "Ready" status. Then, transfer it to another base. Immediately after it arrives, tell it to go to a random point on the globe (preferably where you have no bases) and have it patrol in the area. Clicking on it will show that its fuel tank is 0% full. This ship will now have unlimited fuel until it returns to base. This works best on Firestorms, as they have the same number of guns as the Avengers yet cost less.
Note: After downing a UFO, this ship will automatically head back to base. Be sure to send it on patrol again before reaching base, or you will lose the unlimited fuel feature. Because of this, it helps to keep it patrolling as far away from its base as possible.
Free Manufacturing
In the Workshop screen, choose an item to be manufactored, but assign no engineers to it. Also, make sure it's set to produce 0 of the item. Click OK, then go back and assign as many engineers as you want (preferably as many as possible). This time, change the quantity to 1. When the production is finished, you will have gotten one of the selected items--for free! Doing this with tanks and then selling them works wonders on your finances.
Note: Although it may be tempting to create fleets of free Avengers like this, you must still have adequate hangers, severely limiting your options. Still very useful, though!
All Terror Missions During the Day
During the night, the aliens have a severe visability advantage over your soldiers. I'm sure every X-Com player has fallen victim to a night-time terror mission at least once. Those days are now over. When a Terror Mission comes up, simply equip a Skyranger with all the manpower and firepower you'll need to defeat the aliens, and have it patrol just beside your base. (Game) minutes before the hour changes (e.g. at 1:56), have the Skyranger target the Terror Site. After the hour changes (e.g. at 2:03), have the Skyranger patrol in place again. Repeat this before and after the hour changes until daylight. You see, Terror Sites only disappear on the hour, and they won't disappear if they're targetted by a craft. So if you make sure it's targeted as the hours change, you can stall for time until daylight!
Note: Or, you could just use Scott T Jones's wonderful tool known as Xcomutil. Running the RunXcomW.exe program allows you to make all missions in the light of day, regardless of actual game time. A lot easier to use Util. . .