I searched and found a few posts about shimmying, but I couldn't find the one I was looking for...
My car shakes from around 120km/h to 160km/h under acceleration. If I coast at 120-140 it will still shake (really brutally at 140, too) and it goes away from 140-150, but comes back again from 150-160. Under acceleration, the whole thing is worse and it shakes bad. It'll rattle my dash and shake my mirrors, but I feel it more in the steering wheel then in the seat.
...what does that mean?

when you hit the brakes hard does your car pull to one side? you might just need an allignment

i had this problem, and the solution was a change in tires. i had stock 92 eclipse 14's on, and the tire was pretty worn out. i just recently put on some stock 17 inch GSX rims with a 50 series tire, and the car is smooth as hell...no rattling whatsoeva.

Hitting the brakes... doesn't really dive to one side. I tried going quicker then 160 to see if it really went away but it just gets worse and worse so I don't really go fast. Braking it doesn't dive... it follows all the ruts on the road when I do that but it doesn't dive on good pavement. It doesn't feel like my brakes are applying evenly though, almost like my wheels are square.
The car was sitting for two years before I got it, on the tires I am using currently. They only have 1,700kms on them but maybe they got flat spots? I took it in for an alignment just a little while ago and they said it was good. Maybe my wheels need balancing?

well.. sounds like you're from canada? or atleast not in US?

if from canada, where at?

you need to get them balanced... flat spots can occur but at the same time I've seen cases where they don't. Check for it anyways.

Also check all the ball joints.