A few of my favourites:

Three Days of the Condor: Shades of Le Carre, but lacking the gloom.

Galaxy Quest: By Grabthars' Hammer!

Down Periscope: A little-known Kelsey Grammer vehicle which combines comedy with a rattling good yarn

The Princess Bride: Straight-faced silliness delivered with panache.

Don't Lose Your Head: The 'Carry on...' gang playing silly devils with The Scarlet Pimpernel.

Finally, Doc Savage: The Man of Bronze and The Shadow. If only because, unlike the ridiculous Green Hornet, the casts of these two pulp-based films managed to play it more or less straight!