Q:

Is it possible that people perceive time differently than others do? 

All of my life I have been told to be more patient, to stop "racing through life", etc.   Happily, I am finally mature enough to accept that as solid advice, but I am curious as to whether it is possible that I perceive time differently than others do. 
Today, for example, I was stuck at a red light in traffic on a road that was three lanes wide.   I was in the second row of cars that were stopped at the intersection.   When the light turned green, it seemed to me like 10-20 seconds elapsed before any of the three cars in the first row began to move forward.   Obviously, it is unlikely that all three cars in the front row reacted this slowly--hence my question. 

A:

Short Answer
Yes.  People estimate time differently, by focusing their attention on time in more or lesser degree.  Also within a person, time estimation may vary due to stochastic variations.  
Long answer
This is a really nice paper that tries to explain time-perception in a cognitive architecture called ACT-R. It is a model of human cognition that tries to explain human behavior with only basic functions (declarative and procedural memory, vision, working memory a.o.).  
Very shortly, the model is as follows: There is a pacemaker.  This pacemaker creates pulses that are counted and saved in memory, and this memory is coupled to a particular time-frame.  Each time you start counting, you reset the pacemaker to zero.  So, for instance, after some practice, you learn that five seconds consists of 23 pulses, and eight seconds is equivalent to 30 pulses.  
The pacemaker has two properties however.  First, the pacemaker is not perfect.  There are minor variations in the duration of each interval between the pulses.  Five seconds may thus sometimes be perceived as 22 pulses and sometimes as 24 pulses.  This is the reason variability exists in time estimations.  
Secondly, the duration of intervals between pulses increases over time.  Where the time between a pulse may be 200 ms (+- random value) when you start to count, it may be 400 ms (+- random value) after ten seconds.  On top of that, the effects of random noise also becomes larger.  If you count the pulses, the precision of the counting will thus decrease.  Therefore it is increasingly difficult to estimate longer periods of time as compared to shorter periods of time.  In figure 2 in the paper, this is depicted with the increasing width of the normal distributions.  
Attention
So far I have only explained how one person may perceive time differently due to stochastic differences in pulse productions.  What I left out so far is the attentional component of the model.  When you focus your attention on the pulses your estimates will be rather good, because you perceive these pulses more consciously.  However, as anyone may know, "time may fly" (when you're having fun).  This is believed to be caused by the lack of attention to the pulses, therefore being unaware of how time passes.  It is however not entirely clear how this attentional component works, and the debate is still ongoing.  
Neuro-biology:
The model was based on a paper written by Mattel and Meck (2004), which provide a neuro-biological explanation for the pacemaker.  The model they propose is the "striatal beat frequency model", which states that there is neuronal activity oscillating at different rates in different networks of neurons.  The oscillations are then detected by Striatal Spiny Neurons, which result in a sort of "barcode"(i.e.  an array neurons being active and inactive; see Figure 1A).  It is these barcodes that are memorized and associated with a particular duration (See Figure 1B).  

Figure 1: Striatal beat frequency model.  Picture taken from Researchgate
As mentioned earlier, the pacemaker needs to be reset when you start counting from zero.  It is theorized that this is done by a burst of dopamine.  
Here is a review about the neural pathways for time-estimation by Buhusi and Meck (2005).  My neuro-biology is a little rusty though, so if there is anyone that could comment/elaborate on this, that would be highly appreciated.  
References
Buhusi, C. V., & Meck, W. H. (2005).  What makes us tick?  Functional and neural mechanisms of interval timing.  Nature reviews.  Neuroscience, 6(10), 755. 
Matell, M. S., & Meck, W. H. (2004).  Cortico-striatal circuits and interval timing: coincidence detection of oscillatory processes.  Cognitive brain research, 21(2), 139-170. 
Taatgen, N. A., Van Rijn, H., & Anderson, J. (2007).  An integrated theory of prospective time interval estimation: The role of cognition, attention, and learning.  Psychological Review, 114(3), 577.