While very few movies seem to capture the complexity of the contact period I really like a film called Black Robe. The film follows a 17th century Jesuit father on his travels to Huron missions in Canada. With the exception of the Iroquois/Haudenosaunee, there isn't a big bad in the movie. Both the French and Huron are equally confused by the other's culture, religion, and language. The French aren't all powerful like you typically see in contact period movies, and their influence is limited to a few small outposts. The movie touches on the war between the Huron and the Haudenosaunee, the torture and taking of captives (though it does get some things wrong, the Haudenosaunee would very likely not kill children in favor of adopting them), and the impact of disease spread during the Huron diaspora. The film also touches on faith and belief as the protagonists travel further upriver. Finally, it is quite beautifully shot with amazing landscapes. I need to re-watch it now that I know more about the period, but remember really liking the movie the last time I watched.

I'm specializing in Medieval Hisotry with a minor in Medieval Latin, and I've got to say some of the best novels about that period were written by Italian semiotician/philosopher/scholar Umberto Eco. I know that he's very well known and kind of an obvious answer, but very well deservedly so. His most famous novel, "The Name of the Rose" actually first awakened my interest in medieval literature and philosophy. For those who don't know it, it's a crime novel set in an Benedictine abbey in Italy during the Franciscan apostolic Poverty Dispute in the 15th century.
Eco wrote an excellent essay on medieval aesthetics, and it is especially that part which really makes the middle ages come to live in this book. There is one particular passage that was kind of an eye opener for me in which the young and somewhat naive first-person narrator describes stepping into a church through a big, intricately carved stone portal (the real life reference Eco used is the magnificant late Romanesque portal of Moissac Abbey, by the way). As members of a modern society basically bombarded at every step with images, it's hard to imagine what the sight of giant stone structure with such strong, expressive imagery would do to someone in whose world images would be rare and precious.

And while William of Baskerville, the book's inquisitor-turned-"detective" protagonist may feel a bit too progressive and modern for the 15th century, the ideas expressed by him and the other monks, the way they argue and the way they understand and interpret their world are given a lot of room in the book and feel really "authentic". As someone who is really interested in medieval philosophy, I enjoyed that book tremendously. Even though the movie is good, they cut most of the parts that I liked best in the book - quite understandably, I guess. What movie audience would like to see a half-our debate about the poverty of Christ or the true nature of knowledge?

Some of the best historical fiction I've ever read is Patrick O'Brian's Aubrey-Maturin books. He is so adept at texturing the culture and day-to-day of life in the Royal Navy. It really has the feel of an author that lived his life during this time. I'm not an expert on any historical period but these books have been a great conversation starter with people who are.

I've only read part of it, but Aliette De Bodard's trilogy Obsidian & Blood depicts Aztec culture and religion quite well, I think. Her books include actual magic and interaction with deities, but besides that describing ritual acts and facets of the religion is very entertaining. She brings to life what normally is rather flat in the pages of journals and books.

Any suggestions for WWI?

Edit: Guess I'll read or watch All Quiet on the Western Front.

I was trying to think of a good example instead of just laughably bad ones (Homeland) and I have to go with Battle of Algiers. It's an amazing film: http://youtu.be/Ca3M2feqJk8

Algeria isn't a specialty of mine but in the context of terrorism, occupation, a security state, revolution, etc. it's flawless.

Stanley Kubrick's Barry Lyndon. The 1975 period piece may be a work of historical fiction, but has to be seen to be believed - it is honestly like stepping through a portal to 18th century Ireland, England and continental Europe in the Seven Year's War. I have never seen another film so convincing in how it suspends disbelief.

A lot of what helps is that the cameras had NASA lenses that were made to work with natural light and candlelight, giving the film almost eyesight realistic screen quality in terms of cinematography.

Ivo Andric's The Bridge on the Drina is set in my period, but several hundred miles too far south. The first few chapters make it one of the few novels set in the period that doesn't heroicize any particular ethnic or religious group, but instead tries to show the complex, conflicted, and often contradictary nature of inter-ethnic relationships during the early modern period in Eastern and Southeastern Europe.

There's supposedly a Serbian-language film version in the works, but it seems to have been stuck in development hell since 2011 or so.

Honestly anyone who studies Russian history is spoiled for choices. Mikhail Bulgakov's White Guard would be my pick to convey the confusing and terrifying atmosphere of the Russian Revolution and the Civil War. In film, Miklós Jancsó's 1967 The Red and the White is one of the only war films I have seen that actually portrays war in all its unromantic and pointless horror.

Come and See, a movie by Elem Klimov.