I wouldn't say I'm a big fan but I must have seen the majority of his films when I was a kid (there must have been at least one of his on a week!). I suppose my favourite one's would be...
They were expendable (1945)
The Quiet Man (1952)
The Wings of Eagles (1957) a childhood regular watch!
Rio Bravo (1959)/ El Dorado (1967) virtually the same film! apparently some suggest Rio Lobo (1970) is very similar as well but I could never see it myself...
North to Alaska (1960) great fun!
The Longest Day (1962) a long all-star film that really works.
