Q:

Why do the Mars rovers move so cautiously?

All the Mars rovers tend to move very slowly. For example, Curiosity moves at an average speed of 30 metres per hour and a maximum speed of 90 metres per hour. Why is this so? Is it because of safety reasons? Does the time lag between Earth and Mars necessitate such caution? Then again, the rovers are equipped with hazcams to avoid accidents.
Alternatively, do they travel so slowly for reasons of stability? Does the science equipment on board have such requirements?
Or is it simply because there is no need for haste? How much time does the Curiosity spend idle as it moves from one location to another?

A:

The main reason for the MSL driving slower than physically possible is hazard avoidance (and also navigation/visual odometry):
Source: Introduction to mobility for MSL Heverly, Matthew C. 10-Sep-2012
Hazard avoidance and navigation
Drive rates (m/hour):
Absolute top speed:   151.2 (On rigid terrain with zero slip)
Blind drive:          139.5 (top speed for straight driving
                             with pause between steps)
Blind drive
with slip checks:     116.0 (Averaged over a significant number
                             of slip checks)
Visual Odometry (VO):  64.5 (At every step, look around, 
                             see how far the rover has driven)
Autonomous
navigation (Autonav):  40.1
Autonav 
with slip checks:      38.5
Autonav with VO:       30.0 (Assumes VO driving rate with 
                             additional time for map imaging 
                             at the appropriate spacing)

What is Visual Odometry? Taking stereo images "before" and "after" the step to track true motion, calculate slip and embedding. Accuracy of VO is 3% of the step distance, so you wouldn't want steps to be too long.
Why is it capable of moving slowly?
Actuator design constraints
The mission design logic (see http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/38317/1/03-2974.pdf) is as follows:

Interesting landing site => Technically feasible landing error ellipse => Traverse length
Number of samples
Nominal mission duration (one martian year)

Hence, $Nominal\ Speed = Traverse\ Length/(Mission\ Duration - Number\ of\ Samples * Time\ per\ Sample)$.

