"It's kind of like little kids on the playground: 'I'll show you mine if you show me yours,'" Webber said.
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In recent years, it's also become easier to find out what your co-workers are generally making, thanks to a host of employment websites in which people post their salaries along with company reviews and other information.
Having more information about your peers' salaries can be helpful in negotiating a raise, said David Lewin, a professor emeritus at UCLA's Anderson School of Management who has studied compensation extensively.
Lewin noted that CEOs and other top executives—whose salaries are usually public if they work for publicly held companies—have managed to push their salaries up higher and higher over the years by comparing themselves to their peers at competing companies.
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But, he said, it can be less helpful to know you make less than your peers if you just feel bad about it, and don't ask for a raise. And it could also backfire if the employer does grant those raises, but then takes away other things, like paid vacation.
"It really becomes a question of what someone does with the information," Lewin said.
He said the executive order could help some people feel more comfortable discussing wages, but he doubted it would have a significant impact on most people's pay.
"It might have a marginal positive impact," he said.
The executive order will only apply to people who work for federal contractors, and comes amid other, so far unsuccessful, efforts to get Congress to take similar actions to address the pay gap.
Women earn about 77 cents for every dollar a man earns, according to the U.S. Census Bureau, and that disparity has stayed relatively flat for years.
Researchers have been looking closely at why even women and men in the same profession sometimes earn vastly different wages as well as why that wage gap generally seems to widen as women reach their mid-30s.
One area researchers have focused on is whether women are as likely to ask for a raise—or even a higher starting salary—as their male counterparts. Some research has shown that it can actually hurt women to ask for more money, because they are perceived as greedy, demanding or just not very nice.
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Webber, the human resources consultant, said he only sometimes receives questions or complaints from readers of his advice blog about co-workers who earn more money.
"It does not come up nearly as often as people who think their co-worker smells bad or is being rude," Webber said. "Behavior is something they talk about more than money."
—By CNBC's Allison Linn