Adore emeralds - I seem to be amassing a collection of fake ones. My bucket list includes owning a real Depression-era emerald statement ring someday (like something Wallis Simpson would have worn before she became the Duchess of Windsor). I have a fake one in the style I want, but would prefer to have a real one all the same.
I also love amber - not technically a stone, but who cares? I get real amber instead of fake, though, so that collection isn't as large.