Ron Goodwin’s “Aces High,” main theme from The Battle of Britain (1969):
John Williams’ Midway (1976):
Excellent suggestion!
Bernstein’s music is fantastic!
I didn’t know this was one of Mancini’s:
Right on! 
Funny, innit, that Janet Leigh, who sets the whole story in motion, gets only an “and” credit in Pyscho? That’s what happens if you get bumped off in the first half of a movie… 
Easy Rider (1969) - Steppenwolf
Pit Stop (1969) – The Daily Flash
Repo Man (1984) – Iggy Pop
Well if we’re doing Easy Rider
And finally from my favorite score of all time
ooops couple more. Judge Roy Bean these is so fucking good, Tarantino used it in his last film
Oscar-winning theme from Working Girl (1988):
Theme from John Carpenter’s Dark Star (1974). There’s an “unofficial” third verse in Joe Bethancourt’s performance on YouTube.
We could make a 100 Carpenter posts AND Morricone’s The Thing work.
Did you know there are at least two versions of the Five-O theme with lyrics? (Three, if you count Nick the Lounge Singer’s version, which used to be on YouTube, but I can’t find it now.).
While Sammy’s version might be more appropriate for a gritty cop show, I must say I prefer Don’s. 
John Williams’ Superman theme.
And then there’s the Aussie.punk version…
The original TV version was brilliant, but it got butchered for the movie. Someone hit it with a rock until it was in 4/4 time instead of 5/4
Also great, but from that movie I prefer The Ecstasy of Gold. It starts at about 0:45 in this clip:
From The Sting, I’m partial to “Solace”.
The Battle On The Ice, from Prokofiev’s music for Alexander Nevsky
The Sea Hawk - Korngold
North by Northwest - Bernard Herrmann
Battle of Agincourt from Walton’s music for Henry V
Genevieve - Larry Adler
Things to Come - Arthur Bliss
I thought of posting this (it’s great!), but a vocal version is featured in the movie.
This performance (live in Venice, 2007) gives me the chills:
Magnificent!
Morricone was supposed to do an American tour in 2014, and I splurged on a fourth-row ticket to see him in New York. I imagine it would have been something like that video, and I was really looking forward to it. He had to cancel for health reasons, though.
Someone mentioned John Carpenter, surely “Assault on precinct 13” is worth a mention
And memorably used in “megablast” by Bomb the Bass (and close to my heart as an early Amiga user, it was the theme to Xenon2)
Of course Vangelis has to get a look in here as well, “chariots of fire” is very obvious but I think “conquest of paradise” is a theme that captures the spirit of the respective movie perfectly.
I am so glad you brought up Vangelis! This theme is from a great but vastly underappreciated movie with a wonderful cast:
It too gives me the chills!