The most impressive cases of natural phosphorescence (if it continues to glow after you take the energy source away, it's phosphorescence) are UV-activated and emit in the visible light spectrum, so you need a blacklight.
My husband collects minerals and has a few (stuff like fluorites and calcites, which are actually quite common and cheap).
The Natural History Museum in London has (had?) an exhibit in the jewel vault which contained a whole range of different coloured diamonds, some of which are phosphorescent. That's pretty impressive.