I always though the Space Shuttle needed a combination of its solid rocket boosters and its main engines to remain stable while launching. The following diagram found on Wikipedia seems to agree: after liftoff, the Shuttle tilts backwards to get its center of mass in line with the direction of thrust of the SSMEs. By the time the SRBs run out, the Shuttle and its drop tank are properly aligned for that configuration. Some time later the SSMEs are cut off, and the drop tank is separated. This concludes the "launch"; what remains are orbit insertion burns, doing what they went up for, and returning.
When I recently saw someone with a T-shirt depicting a Space Shuttle launch with the SRBs firing, but the main engines not showing any exhaust, I thought that was an error in the drawing. However, I've since come across this picture, which shows a launch with the SRBs very much active, but no visible exhaust plume from the main engines:
Is this simply an issue with the relative brightness of the exhaust of the big barrels o' fireworks vs. the exhaust of the liquid fuel engines, or are the engines effectively off in the picture?
For context, pictures in an answer to another question on this site make it very plausible that the SSMEs simply produce less soot and light. A picture on the NASA website also seems to show SSMEs which are 'on', but not very bright in comparison with nearly burnt-out SRBs.