I've never seen it go bad. Even the super-cheap stuff that comes in a bag doesn't dry out once you open it.
Otherwise it would pretty quickly go bad after application... I tend to go for moderately priced stuff that's reasonably easy to use. Unless you're a competitive overclocker looking for that extra half a degree they are much of a muchness once you upgrade from crunchy peanut butter or mayo. I always keep a tube knocking around, never know when you might need some. I never spend much more than a tenner for a larger tube.
in the hot as heck southeastern USA I have seen it start to separate, out in the garage I go to goop something and get clear liquid then silver gunk then wipe it off, but its only at the very tip