This sounds like something we'd all like to be able to claim, complete with spandex suit and billowing cape! Especially since the opposite is, unfortunately, called a nontaster or undertaster, when in fact neither is better than the other, just a difference in perception.
Google "supertaster test oz" or see the Wikipedia entry for supertaster for information on the several ways to test yourself, and the implications for your dietary health. One is to put a packet of Sweet 'n Low (saccharine) in 5-6 oz of tepid water and taste. If it's strongly sweet, you are a non-taster; a mild mix of sweet/bitter, a regular taster; very bitter, a supertaster. Supertasters tend to find coffee and vegetables - especially brassicas (like broccoli, cabbage) in particular - bitter, so they may be "picky" eaters who don't get good nutrition. Non-tasters (I seem to fit this category) crave sweet tastes more than regular or supertasters.
It is interesting to learn that genetic differences affect our perceptions of certain smells and tastes. It used to be thought that only some people pruduce fetid-smelling urine after eating asparagus. Now science seems to think that everyone does, but only some people can detect the smell. There are genes that make musky smells attractive to some noses but repellent to others. The useful lesson here is that trying to "educate" a loved one to appreciate a flavor s/he loathes may be a hopeless task. While we often DO come to like foods that are "an acquired taste", it's not inevitable.