The look your getting is called "micro jitter". If you plan on shooting video on the 7D's, T2i's or 5d's drop the money on lenses. Not every lens I have has IS but most do for a good reason.
Watch this video and you'll see the difference which is the exact look your getting. IS works similar to a motion tracking software but inside your camera and lens. It's not going to make it look perfect, but should help a ton. Obviously not every lens I have or everyone has will have IS but alot of the quality shots with heavy movement that look smooth won't have that microjitter because of IS. IS stands for Image Stableizer.