Mad Men
There are few characters that have displayed overt political philosophies, and a number of them which I assume may be a political. Given their residence in New York, their vote narrows it down. Went with '64, and pointless not to include primaries--though that does mean there'd be an NY primary, and I don't believe there was. 
1960 would be interesting as well.
Don Draper: Didn't vote. Seems to be a political.
Bertram Cooper: Goldwater - Ayn Rand fan!
Roger Sterling: Rockefeller - When he hears about Rocky's divorce, he's pretty upset that all they have left is Goldwater.
Peter Campbell: Rockefeller - Comes from money. Only clue.
Peggy Olson: Goldwater - Only one clue with this one, where she says in Season 4 that she'd like to have worked for the Goldwater campaign.
Paul Kinsey: Johnson - Got all "New Left" on us in Season 2 and went to register African-American voters in Mississippi with his African-American girlfriend.
Betty Draper/Francis: Rockefeller - Indicated a preference for Nixon in 1960, plus by Season 4 she's seeing someone working for Rockefeller. Best guess here.
Henry Francis: Rockefeller - Duh! Works for Governor Rockefeller and later "the Congressman", John Lindsay running for Mayor.
Stan Rizzo: Johnson - He worked for the Johnson campaign, of course.
I should do 1960... Also, apparently the most recent season goes up to '68, so maybe we'll see that.
RE: Peggy: In that exact same season 4 scene where she says she would have loved to do ad work for Goldwater, she says she voted for Johnson. And we know in season 1 that she likes Kennedy as he is Catholic. In season 6, she says to her boyfriend Abe (a Eugene McCarthy-ite) "I like Bobby Kennedy..." an episode or two before he is shot. That last one is one of my favorite Peggy line reads. Also, Peggy has a portrait of JFK in her apartment for most of the series. If Mad Men were running for another season, I wouldn't be surprised to see a storyline where Peggy gets involved with Shirley Chisholms campaign as many women in NYC did.
As for Pete, he definitely voted for Nixon in 1960 but in a season 6 scene he says with disdain about his neighbor "He voted for
Goldwater" so we can assume Pete voted for Johnson in '64.
I suspect Betty voted for JFK in season 1, but kept it hidden from Don which is the context where she says something about Nixon.
I agree with you about Don, I doubt he voted in 1960. If he did vote in 1964 (which he might have, he was pretty happy that year), he voted Johnson. In the end of season 6, he complains at a bar that Nixon is President, suggesting he doesn't support him. As a veteran Don vehemently opposes the war. I don't think he voted in 1968 either. If he did it was reluctantly for Humphrey.
Roger Sterling definitely voted Nixon in '60 and '68. Not sure what he did in '64.
Bert Cooper has an adorable line read in season 6 where he mischievously says "Nixon's lying in wait," so he definitely supported him in '68.
There's a pretty funny scene in season 6 where Ted Chaugh gets drunk and instigates a conversation about who everybody supports.
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