Paul Ekman had this "theory of basic emotions" that were supposedly universal for humans and had their set of "innate" gestures for each one.
For his original works, he travelled to some secluded communities and registered that the expressions for "happiness / fear / anger / disgust / sadness / surprise" were supposedly shared among human kind.
Why do I say supposedly? Because a lot of Ekman's theory was disproved (for example, he claimed each emotion had an area of the brain dedicated to it, or at least some unique structure, which fMRI studies are not finding to be true, even if there is a lot we still don't know on human emotion). There's also claims that he contamined his data when he went to these secluded communities, and influenced (probably unknowingly) his results to make everyone's expressions match the ones he expected for each emotion.

So... are there universal expresions of emotion? Not an easy answer. The physical responses more linked to survival probably are (say fight/ flight in response to fear, startle in response to surprise). The more social ones? don't know, some may be heavily influenced by culture. You would have to make a study on very young, blind babies from different cultures or something of the sort which would not be easy. Also there's the thing that babies cannot tell you what emotion they are experimenting, even if you can asume some (loud noise and baby is crying probably equals fear, BUT the baby can't confirm it, which is a methodological problem for some Scientists).

If this interests you, Ledoux has some great approachable work on the "survival circuits" of the brain that explain emotion in a way comparable to animals and linked to their evolutional value.