It's an interesting analysis by Mike. I'm going to push it back to 1948, not because I can remember that far back, but because I think that Mike's is an arbitrary cut point.
1948: Truman was an artillery battery commander during WW I and saw action. Dewey was too young for WWI and was Gov. of New York throughout WW II. War Hero wins.
1952 and 1956: Eisenhower had military experience, but never saw combat. On the other hand he was credited with beating Germany. Stevenson had no military experience. War Hero wins. Twice.
1960 As noted by Mike, JFK had PT-109 and Nixon had non-combat WWII service. Perceived War Hero wins.
The party distribution is interesting to me. Since the 60s, the only combat veterans from the Democratic Party ran as peace candidates and all of the candidates with no military experience whatsoever were also Democrats. Too much could be made of this though. For example the only other Republican candidates with military experience were Ron Paul, and Duncan Hunter, neither of which had a snowball's chance.
So what's going on here? Every postwar election until 1960 is won by a war hero, and the only instance since was father Bush, who, let's be honest, was riding Reagan's coat tails. The 1960s. Vietnam. That's what happened. Being a combat veteran stopped being useful, unless you used it to fortify your anti-war stance.
I think that this might be changing. Starting in a few years, Iraq and Afghanistan veterans are going to be entering the field, and given the opinion of much of the electorate of the military, having served will be an enormous plus.