Top Fave: cut, faceted Chrysocolla (NOT cabachons!). I only know one man in America who regularly cuts and facets it into perfectly clear gem stones. The color is absolutely incredible!!! It's a gorgeous milky blue-turquoise shade.
Other Faves:
Pink Tourmaline
Indicolite (another Tourmaline, love this stone!)
Peruvian Opal
Aquamarine (though in terms of a blue stone, I'd love to have a paraiba tourmaline too!)
Diamonds
Rubies, but only if they are a vibrant cherry red color
Moldavite is an interesting fave of mine also