While I have mentioned it before, Tallis' Spem in Alium deserves highlighting. Composed for 8 choirs of 5 parts each (40 parts) in 1570, it was said to have won Tallis a gift of gold from a duke at its performance. The text is here, in English and Latin.
There are many other beautiful choral pieces which could be considered "epic," such as Sicut Cervus or Deo Gratias, and I encourage you to investigate them.
There are many Russians known for epic music - Tchaikovsky's 1812 Overture being a famous example. One which I particularly enjoy is Mussorgsky's Pictures at an Exhibition, a suite based on pictures drawn by a friend. Originally composed for piano, it has been orchestrated by several different composers, including Ravel, Henry Wood, Leonidas Leonardi, Stokowski, and Askenazy, among others. Below, I have placed two videos - the first with Evgeny Kissin on piano (Hut of Baba Yaga and Great Gate of Kiev), and the second, by Theodore Kuchar and the National Symphony Orchestra of Ukraine.
Another epic piece of music is found in Ottorino Respighi's Pines of Rome. A tone poem comprised of four different sections, Respighi composed this in 1924. The fourth movement, the Pines of the Appian Way, is intended to represent:
[A] portrait of the pine tree-lined Appian Way, the military road of the Roman Republic. The Roman legions emerge from the mists, and the orchestra mirrors their approach, growing louder as the soldiers get closer to the Capitoline Hill. As the movement closes, the victorious warriors, led by the Republican Consul, arrive at the Capitol with the rising sun behind them, their glory reflected in the work’s jubilant closing pages.Without further ado or dissembling or blather:
Gorgeous. Did I mentioned that I am not going to discuss Ride of the Valkyries from Wagner's Die Walkure? It's from an opera. Enough said.
Another piece I have mentioned before, but is worth posting again is Ralph Vaughan Williams' Fantasia on a Theme by Thomas Tallis. It was originally performed in Gloucester Cathedral in 1910 originally (as is the below, by Andrew Davis), and included Herbert Howells (among others) in its audience.
Aaron Copland is a moderately well-known American composer, friends with Leonard Bernstein, who is remembered for a distinctly "American" sound. I have two pieces for your perusal - Appalachian Spring, which has a "short" and "long" version. I have included the "short" below, and an excerpt from his Third Symphony (itself a lengthened use of Copland's Fanfare for the Common Man).
What else..what else...let's see...
The finale to The Firebird by Stravinsky merits consideration (esp. after 7:40 or so)....
Alexander Nevsky by Prokofiev deserves a listen (excerpt below):
I know I have skipped over many here - what are some of your favorites?