Friday morning, I woke up early to change handlebars on my road bike before I left for work - again. Last week I had put on a different set of handlebars, looking to get a deeper, lower position than my preferred handlebars, Ritchey Biomax bars, afforded me.
I first realized the importance of handlebars and bike fit a little over a year ago, when, after many rides fidgeting and trying to get comfortable on some deep, square-ish ergo drop bars, I picked up those Ritchey bars because of their shallower drop, slight flare, and what I thought would be a more comfortable angle of the ergo section. I realized that the reach was shorter and that given the incredibly wide variety of handlebars, choosing the right handlebar was as much a matter of proper fit on the bicycle as was installing the right length stem. When I discussed bicycle fit with people - especially people for whom bike fit is somewhat tricky, like short people (like myself) - I would always bring up handlebar choice.
This became additionally important when I saw how many entry-level track racers fit themselves on track bikes. I saw a lot of people riding very close and deep; their arms went almost straight down to very deep drop bars. When I bought my Felt, one of the first things I did was give away the ultra-deep Deda drop bars and get Nitto B125s, shallow-drop track bars that are comparable to criterium bars; I recently put on a 120mm stem. My drop isn't extreme and I'm reaching out to the bars a bit more than I'm reaching down to them - it's a stable, long fit that I feel gives me good weight distribution, a good diaphragm-opening reach, and an aero enough posture, without compromising the bike's handling.
Considering my discovery of the importance of handlebar ft, I was pleased to come across this site, which has animations of the different geometries of different drop bars, illustrating the significant differences in reach and drop that different types of handlebars afford. With longer-reach bars having perhaps as much as 3 centimeters more reach than others (which was the case with the bars I just removed from my bike), it's important not to neglect this aspect of bike fit - as much as it's important to not arbitrarily use an 80mm stem rather than a 110mm.
It doesn't necessarily take an experienced and expensive fitter to get yourself comfortable on the bike, although the cost/benefit of that might work out in your favor if you're looking to align optimal comfort with optimal performance, with some other difficult variables thrown in. An amateur can play around by looking at other people's fit, experimenting with saddle position, stem length, and, of course, handlebar dimension.