Alien movement patterns
Closely linked to Spawn Points are the alien movement patterns (aka routes). Although the maps are randomly generated, each module (especially ones with doorways) have patrol points defined. Aliens on patrol will follow a route through these points until they spot the enemy (you). Then the aggression formula takes over.
There's a safe method to dealing with almost every UFO. Due to odd positioning, some ship have alien 'guards' that do not move from their spot until you 'trigger' them somehow, either by walking through a door or standing at certain locations in the UFO. In general, they'll head in the general direction of the nearest soldier to them.
[ Hobbes: This is debatable - When the AI is moving an alien it can happen that the next waypoint is already occupied by another alien unit and thus it will freeze on its location without moving. In those cases what will happen is that the alien will wait until the path is clear before moving.]
The Large Scout sometimes has a nasty one, depending on the exact location where the alien spawns in the bridge. Stepping through the right-hand doorway when approaching the bridge (relative to the screen, this is the upper passage) will usually get you killed instantly.
The best way to deal with this guard is by setting up an ambush outside the left-hand door. Moving into the corridor outside that door will dislodge the guard, who will then come to you. By the next turn it should be in the room just beyond -- exhausted and unable to fight back. On Superhuman settings, a roused Sectoid guard will have enough TUs to step through the door, and you must arrange your troops to minimize reaction crossfire once the alien appears.
Thankfully, movement within the Large Scout's antechamber will not dislodge the guard -- only movement into the left and right subchambers will. You can preserve your TUs by moving your troops up against the wall opposite the UFO outer door, then arrange them facing the inner doors on the next turn.
Other UFOs may require bigger weaponry to deal with these 'guards'. The Abductor for example has a guard that always waits in the centre of the bridge. It's untested, but it may be possible to get this guard to face in a different direction by placing a soldier as close as possible to it and ending the turn. On the next turn, have a soldier barge through the door. Again, this is untested, so use it at your own risk. More practical solutions to this include cutting a hole through the rear or floor of the room with a Heavy Plasma, deploying a smoke grenade in front of the door, stepping through and launching a rocket or a grenade, or even just standing underneath the alien and firing a high explosive weapon directly at the ceiling.
The Terror Ship has a pair of open-floor hiding places just above the corridors connecting the outer pods to the main body of the craft. Any armed alien stuck up there will have plenty of TUs available to gun your troops down as they walk underneath.
It is usually safe to approach these hiding spots by hugging the north wall of the corridor until you step just inside the main saucer, then pivoting north to see what's hiding up there. The alien will not return fire when you are in this position, most likely due to the elevator shielding bug.
Floaters and the Koan of Stairs
Floaters might know how to go up stairs, but they certainly don't know how to go down them.
Eventually, the hapless floater will have the AI try to route it from the top of a staircase to the bottom of the same staircase. Unfortunately, not having legs, the art of walking down stairs escapes the floater. With a few precautions to abuse line-of-fire bugs, this makes the stuck Floater easy prey for even a lone X-COM agent.
Note that a similiar situation will occur with Mind Controlled X-com agents in flying suits. The AI knows how to walk them up a staircase, but cannot walk them back down. For player controlled units, IIRC, your units will have to find an alternate route or shoot the stairs then fly down, or other similiar workarounds.