Almost any part of the body can be pierced, although not always with complete success. The more common piercings are popular for a reason they have been performed and worn successfully by many people. Most are fairly easy to heal and care for, attractive, and fun.
The old cliché "if you can pinch it, you can pierce it" is largely true. The exceptions are those few locations where you can't reasonably protect the piercing during healing (such as the sole of a foot), or where the tissue is delicate and likely to be damaged during normal wear (like the eyelid). Yes, you will see people with "impossible" piercings, but they are taking a dangerous chance.
Even common piercings aren't suitable for everyone. Some depend on the individual, a willingness to make concessions on activities/ clothing during the healing period, or health concerns. We encourage you to speak up about any concerns you may have before getting your piercing. In particular, if you have allergies, a condition which affects your immune system or ability to heal, or if you are (or are planning to become) pregnant, please tell us. Virtually any problem can be resolved by alternative methods, timing, or materials. . . but only if we know what you need.