Real cultures are not monolithic, overarching creeds that define every single member. Individuals and sub-cultures break from the mainstream and create little pockets of different traditions, regional cultures, and countercultures. This is how the real world works, but most fantasy world-building treats an entire race or nation as a single culture. Digging deeper makes the culture more interesting, and exploring sub-cultures counterpoints the mainstream culture and makes it more interesting as well.
Roleplayers can fall into this quite easily, both in traditional tabletop as well as in MMORPGs. Truth be told, so do ‘professional’ writers, which explains why minority actors frequently have trouble getting non-stereotyped roles.
In some games, players restrict themselves even further: not only must a Wookiee excel in hand-to-hand combat, he must fight for the Rebellion and call himself a madclaw. The most interesting characters, of course, transcend this. I recall reading advice many years ago about playing characters from ‘monstrous’ races, to the effect that while your character doesn’t have to share the characteristics or exhibit the behavior typical for his race, he should have thought about the fact that his race does have that reputation and have an opinion on it.
Do your characters fall into stereotypes because that seems easy? Not that playing a ‘typical’ character is somehow wrong (as if that even could make sense), but if you do so, I suggest that you do so as a conscious choice rather than as a lazy default.