Just to add a bit more to the mix:
Kenji Tomiki had an interesting perspective on Atemi, which is probably a bit different to most of the definitions that have come up so far.
The way he saw it aikido techniques basically fall into two categories, atemi waza and kansetsu waza. And in trying to come up with a safe system of 'competitive' randori, he saw two distinct ways to classify them:
" 1. The atemi-waza control an opponent by hitting, thrusting into, or kicking the physiological weak points of the body; while the kansetsu-waza control an opponent by inflicting a sprain or dislocation on a joint. That is to say, these techniques were devised with the purpose of maiming or killing, and so are fundamentally dangerous.
2. The atemi-waza topple an opponent by applying force to the mechanical weak points of the attacker's body in order to gain kuzushi, the breaking balance, and then push him over; while the kansetsu-waza restrain an opponent with a minimum of force by utilizing the limits of joint movement to pin the opponent down. "
The first category are probably the atemi waza that most aikidoists think of as 'atemi', but in the terminology used in Shodokan a lot of important techniques are classified as atemi-waza of that second variety.
A couple of examples are irimi nage and tenchi nage (both varieties of aigamaeate in Shodokan terminology), and sokumen irimi nage (gyakugamaeate). And if you think about tenchi nage for example, you can see how it might fit into the first category too - sure your 'heaven' hand can go over uke's shoulder, but it can just as easily smash into uke's face.
ps: The quoted bit is from Fumiaki Shishida and Robert Dziubla's 1986 translation of Kenji Tomiki's essay "On Jujutsu and its Modernisation"
from the JAA/USA website. -I'm sure its on the Shodokan Honbu
website too, but since it was revamped I can't seem to find it.