You can do this with more than basil too! Mint, lavender, thyme, rosemary, lemon verbena, sage and oregano are all easy to root. This could be a great and easy gift idea. You can simply buy pots, root your herbs and start an herb garden for a friend, all for the cost of pots! Or what a great idea for a get together? Every bring some stems and swap!
If you are a detail person, here is a great article on the many ways to grow herbs from stem cuttings.