Yes, Out of the Past is the flashback-y one with Kirk Douglas. Thunder Road, as has also been mentioned, is great. El Dorado is also a fun western (it's a Rio Bravo remake with Mitchum in the Dean Martin role and a young James Caan in the Rick Nelson role) if you can deal with John Wayne and one scene of absolutely jaw-dropping racism.
I know Mitchum played Phillip Marlowe a couple of times in the 70s but I haven't seen either.