As often as we say "beggars can't be choosers", we, as a species, can be very choosy indeed. When it comes to things like food, we tend to select what we consider the best of the best, and reject the rest.
We do the same with data. With both what we consume, and what we share with others, we tend to select that which is favorable to us. It's a good strategy when advertising our products. Be it "9/10 dentists recommend our toothpaste", or "4/5 doctors recommend our cigarettes", by presenting the data that is favorable to you, you are more likely to convince people of whatever you are trying to convince them of.
But given the nature of those two statements, it's obvious where the flaw is. Although cigarettes did indeed use to have the endorsement of many doctors, they are now widely known to be linked to cancer. And of course, while toothpaste is good, having the endorsement of a large portion of a presumably small group of dentists does not set one brand above another.
As with most common fallacies, religious debates will often involve cherry picking. As an example, consider radiometric dating. Radiometric dating is often used to cast doubt on the reliability of the Bible, especially when it comes to the origins debate. It is assumed that radiometric dating is nigh inerrant, and thus, since it often contradicts the Bible, the Bible cannot be true.
What is less known to the public, however, is that the "dates" they are given have been carefully selected in order to confirm a given position. As Professor Bruce Brew once wrote, "If a C-14 date supports our theories, we put it in the main text. If it does not entirely contradict them, we put it in a footnote. And if it is completely out of date, we just drop it."
Among the discarded (and occasionally flat out censored) dates are wildly disparate dates from the same sample, ages of thousands of years from freshly dead animals, and even carbon-14 in dinosaur fossils. Evidently, dates are cherry picked in order to give the impression that certain "theories" are correct, when in reality, other data, even from the same techniques, is less favorable to them.
Although there is something to be said for discarding outliers, which may result from erroneous experiment, no data should be excluded without good reason. Thus, the simplest counter to cherry picking is to highlight the "excluded cherries". If no good reason can be given for excluding them, the argument falls under cherry picking, and fails.