Not that I want a tattoo particularly, but if I did then "Blacklight reactive ink" is what I would want it done in. Glows in UV light but is invisible in normal light! Apart from finding somebody local who actually does this, there would be the matter of picking the right design; Apple/IBM/Commodore logo, Quake logo, circuit diagram, Escher drawing, biohazard, radiation symbol, "THX1138", a barcode, "Property of Donna". There are all sorts of ideas for geeks and physics geeks.
Note that not all ultraviolet tattoo inks are equal, some cause nasty reactions so make sure you know exactly what inks the tattoo artist is going to use. Check out Tattoo Health and the PMMA products by BioMetrix/NewWest. And check out the general health issues with getting and maintaining your tattoo from the many sites out there.
Then I would have to go and buy a UV torch. While I was at "United Nuclear" I would just have to get a Geiger counter; a model that detects alpha, beta, gamma and Xrays. You know, so when society collapses after the USA sends its radioactive gifts of love to whatever country has resources that it wants, I can detect if it safe to go outside. Or breath. In the meantime, I could prove to myself that the microwave oven doesn't actually produce ionising radiation, and maybe neither does my mobile phone. Oh, the wireless network is suspect too. That glowing crap I'd like scratched into my skin. Monitors. The backyard. Water. The cat. Babies. Whatever.
Check the article at PostStar about UV tattoos.