Height is often a sign of dominance, as anyone with a Napoleonic complex will be only too happy (well, not happy) to tell you. Yes, powerful people are taller...and when that's not actually the case, they just assume they are.
There's a decent amount of research backing up the assertion that more physically intimidating people - and being tall is one easy way to be intimidating- tend to end up in position of power, regardless of actual abilities or talents. Whether this is an evolutionary throwback or a more recent cultural phenomenon that prizes the very tall, it does seem that height is a good thing to have in today's society.
What's interesting is that powerful people will apparently always find a way to feel tall, even if it's just in their head. That's the recently published finding of researchers at Washington University in St. Louis:
In three experiments, we tested the prediction that individuals' experience of power influences their perceptions of their own height. High power, relative to low power, was associated with smaller estimates of a pole's height relative to the self (Experiment 1), with larger estimates of one's own height (Experiment 2), and with choice of a taller avatar to represent the self in a second-life game (Experiment 3).
The researchers found that these results held true both when the participants were psychologically primed to feel powerful and when they came to feel that way through being assigned roles in the experiment. And consider, we're just talking about people who were made to feel powerful briefly in the context of an experiment. I can only logically assume that people who are actually incredibly powerful must think they're twenty feet tall.
Via NCBI ROFL. Top image from the non-classic movie My Giant.