Why does my car shake driving at city speeds.

Yes and no. If im driving and my car is shaking bad, it still shakes in neutral. When its barely shaking at all, I cant feel it shake in neutral

I bought the car off the used lot. Ive had it 15 months, and I noticed it shaking a few days after I bought it.

Nope. Its been about the same

Its in the steering wheel aswell. My steering wheel doesnt really vibrate thought. Its more of a rapid movement left and right. When I have my hand on the wheel, my hand probably moves to each side about an inch and a half to two inches sometimes. My car and the steering wheel pretty much shake all the time. A third of the time its a really light shake, but the rest of the time it shakes really bad. Also, when it shakes really bad, if I turn a corner, sometimes it goes back to light shake, and it goes back to a light shake too when im slowing down to stop.

Well, I dont know personally, but the service department at the dealership keeps telling me everything is "up to par". They had thought that my car may have been shaking because of what they called "shopping cart effect" so they sent me (4 months ago) over to the body shop to have my front end pulled forwards and to have my car and the parts measured to make sure nothing was bent. They measured the frame aswell to make sure my car hadnt been in an accident like I had suspected. I was told that everything was straight, and the frame was out maybe a mm all around, and they had reasured me that my car was never in an accident. Needless to say, moving my front end didnt fix the problem. But it didnt make it worse either.

Also, my check engine light came on about 2 months ago. The little computer was getting mis-fire codes from all 4 of my spark plugs. I was told that could be a possibility for the reason why my car shakes, but was doubtful. I had changed the spark plugs and the light went off the next day.