A 56-year-old government employee from Cleveland named Tom Pavelka had the "highest credit score in America" in 2012, the Daily Mail reported at the time. His near-perfect 848 ranked "higher than 100 percent of U.S. consumers," according to a letter he received from a credit bureau.

What might a score of nearly 850 have awarded him? The same things you get with any score in the excellent range and not much else, experts say, besides 15 minutes of fame, of course.

"Once you're above 760 you're getting the best rates," Greg McBride, chief analyst at Bankrate, tells CNBC Make It. "That's why obsessing over a score of 800 versus 820 is largely a waste of time."

For John Ganotis, founder of CreditCardInsider.com, the threshold is 750. Anything above that will "likely qualify you for some of the best rates and offers," he tells CNBC Make It.

You can have dozens of credit scores for different types of loans, but they'll all be in the same ballpark, since they each reflect the same credit report. FICO scores range from 300 to 850. While anything below 650 is considered problematic, a score of 700 or above is prime. Once you hit 700 "you may not get the best rates, but you'll typically qualify," says Rod Griffin, director of consumer awareness at Experian. The average FICO score recently hit an all-time high of 704.