I separate mine. I find that if I'm smoking something strong, it doesn't matter much (with the exception of Latakia), but it's when I try to smoke something light that I can still taste the last tobacco I smoked.

I dedicate my pipes as follows:

-Virginia
-Virginia/Perique
-Dark Virginia (like 1792, or Irish Flake)
-Latakia
-Cobs for anything & everything

YMMV