The people who memorize thousands of digits of pi generally strike me as more inhuman than impressive – not at such tasks does the normal human mind excel. Nonetheless, being able to recall ten digits or so might allow you to win bets at geekier parties and, if that can be achieved painlessly, it may be worth doing.
Probably the best way to do so is with mnemonic techniques. You can get fifteen digits by using the number of letters in each word of the following phrase:
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!
Many other examples, including an entire sonnet, are on the Wikipedia page for Piphilology.