We get a ton of inquiries like this from curious women, but the truth is, almost no one gets the clitoris itself pierced. Far, far more sensible, easy, and common is to get the clitoral hood pierced; that is, the thin membrane of skin which covers the actual clit.
Most common is the vertical clitoral hood piercing (a "VCH"). A horizontal clitoral hood piercing ("HCH") is also common. These are commonly referred to as "hood" piercings (not clit piercings).
A clitoris piercing is possible, but it's rare for several reasons. First, it's a pretty extreme piercing, with potential to cause damage to a Very Important and Sensitive Organ! Second, because very few women have clits large enough to accommodate one. Here's an excerpt from The Piercing Bible* about clit piercings:
Piercing of the clitoral glans (visible beneath the hood) is rare, and it is serious business. A piercing mishap can result in the loss of your clitoral sensation . . . only a highly experienced master should perform this piercing . . . exercise extreme caution before embarking upon a clitoris piercing; this is not an area with which to take risks.
Out of the very small number of women who genuinely desire a clitoris piercing (rather than the much more common hood piercing), approximately 90 to 95 percent are not suitably built to accommodate jewelry through the clitoral head.
So, girls, if you are interested in getting a genital piercing, do yourself a favor. Find the best, most experienced piercer you can find, and ask for a consultation and evaluation of your own anatomy. They don't all look alike and the piercing that is best for your BFF may not be the best piercing for you. A hood piercing is an easy piercing that can look and feel great, but a clit piercing is something different.
If you're confused about anatomy, here is a link to Wikip on female genital anatomy: http://en.wikipedia.org/wiki/Clitoris
*The book, The Piercing Bible, by Elayne Angel, is the best reference out there. You can buy it from Tribe.
I'm tired of answering this question, so I'm making this a sticky for now.