Aimed, Snap, or Auto?

Xcom greatly favours "spray and pray" tactics... Auto shot is more likely to hit the target, per [Time Units|TU], than any other firing mode. In fact, even discounting TU, 10 auto-shots will on average score more hits than 10 aimed shots. Snap Shot is gives more hits than Aimed in terms of TU, but of course is less accurate per shot fired.

Auto Shot is also the most useful for destroying cover and obstacles. If the aliens keep ducking back behind a wall or corner, auto shot it! (works better on non alien or Xcom walls, lasers or better needed)

In target rich environments, auto shot will occasionally kill several aliens at once... even ones you were not aware of!

Autoshots also benefit from uninterrupted fire. Single shots are very likely to cause the enemy to make an attack of opportunity if the attacker loses the initiative after making the shot and it does not kill the target (assume the target has all the right conditions to make a reaction shot). Against the AI, single shots will alert AI controlled units and prompt them into making a reaction shot. With auto fire, the same will still happen, but only at the end of the three round burst - never in the middle of the sequence.

Additionally, if the three rounds somehow causes the shooter to get killed, all three shots will still be fired even if the shooter is dead (chronologically).

So, why use any firing mode other than Auto?

One reason is collateral damage. Your Snipers are usually way behind your scouts... often, your scouts will within the firing path of your snipers! So, auto shot here is a good way to achieve friendly fire... making aimed shot suddenly a good choice.

Aimed or snap shot is also crucial when AMMO is a concern. They become much more efficient attack modes with greater accuracy levels. ... Then again, Auto Shot ALSO becomes a much more efficient attack mode with greater accuracy levels.