The ancient Sumerians used multiples of 60, as we continue to do for time and angles (which are related) today. It makes perfect sense. 60 is divisible by 2, 3, 4, 5, and 6, which makes it easy to use in calculations. Even the metric people are not so crazy as to propose replacing these with powers of 10.
Same with pounds, for example. A pound is 16 ounces, which can be divided 4 times without involving any fractions. Try that with metric.
Then there's temperature. Fahrenheit just works more naturally over the human-scale temperature range without involving fractions. Celsius kind of sucks by comparison.