Of course Harold & Maude comes immediately to mind for “most”, but 99% of major age differences in movies are with an older male.
On television the most believable M-D relationship was between Holling & Shelley on Northern Exposure- the actors played off each other beautifully and you actually forgot there was a 40 year age difference between the characters and the actors when they were expecting their baby or curled up in bed, etc… (Perhaps the fact that both of the actors were Southerners playing Canadians helped them bond.)
In film, most believable:
Peter O’Toole & Mariel Hemingway in CREATOR (a bomb from the 1980s though not a bad movie and one that could probably stand a remake) really rang true for me
Richard Widmark & Faye Dunaway (more of an August-December) in Cold Sassy Tree
Least believable:
Burl Ives & Sophia Loren in Desire Under the Elms- I honestly believe that both actors went onto the wrong soundstage one day and they just decided to shoot this film anyway
Woody Allen & Julia Roberts in Everyone Says I Love You
Your picks, please.
Julia Roberts and Nick Nolte in I Love Trouble. (I think that’s what it was called)
Most believable: Lauren Bacall with Humphrey Bogart in To Have And Have Not. He was old enough to be her father, but she was very mature for a 19-year-old. Looked fine to me.
Least believable: Nothing is coming to mind right now.
hmmm a Geezer can’t think of one least believable? How shocking.*
My vote for least believable goes out to As Good As It Gets don’t get me wrong I love the movie but I never bought the romance at all. It didn’t even work as two people getting together out of desperation.
*since I’ve been overusing humorous smilies lately just assume that was light teasing.
Least Believable:
Bob Saget and Mary Kate Olsen in “Full House”
Most Believable:
Charlotte Rae and Mindy Cohn in “Facts of Life”
I think it’s fairly well known in show biz circles that it was actually George Clooney who was the recipient of Ms. Rae’s fading charms. Supposedly the usually calm Clooney still goes ballistic when asked to “talk about the time you were Charlotte Rae’s bum-boy”.
I’m usually calm too, and I don’t think I’d take it well if anybody calle me that. 
And we won’t even get into the ribbing he took over “Edna’s Edibles”.
For “least”, how about Sean Connery and Catherine Zeta-Jones in Entrapment? When I first saw the cover of the box, I wasn’t sure if she was supposed to be his daughter or granddaughter.
Best: James Spader and Susan Sarandon in White Castle
Worst: supposedly, Ronald Reagan and Shirley Temple in That Hagen Girl, I haven’t seen it, but even Reagan didn’t think it was believeable.
Most Believable: Bill Murray and Scarlett Johansson in Lost in Translation.
Anyone remember William Holden and Kay Lenz in Breezy?
::shudder::
Audrey Hepburn and Fred Astaire in Funny Face. They had about as much chemistry as…oh…Pssst! Anyone know a folksie euphemism for “Little or No Chemistry.”?
I had forgotten about Hepburn and Astaire. Yes. Definitely. No chemistry.
I was going to mention Audrey Hepburn and Gary Cooper in Love in the Afternoon. It’s been ages since I’ve seen it, but memory tells me that their chemistry sucked. And I’m a big Gary Cooper fan. BIG. But . . . yuck. An example of terrible miscasting.
Oh, I just remembered: a controversial choice, but I liked the chemistry between Harrison Ford and Julia Ormond in the remake for Sabrina. I know the movie wasn’t as sharp and clever as the original with Hepburn, but I liked it anyway. And I thought the chemistry between Ormond and Ford rang true. I think he was supposed to play a 40-something guy and she was in her 20s? (Ford was in his early 50s when he shot the film, and Ormond was about 30.)
“… they had as much chemistry as Mike Tyson did in high school?”
Most believable: 17-year-old Kirsten Dunst playing 26-year-old Marion Davies opposite 50ish Edward Herrmann playing 60ish (I think) William Randolph Hearst in The Cat’s Meow. The movie has serious creep potential, but Davies and Hearst’s relationship is viewed sympathetically. Their interactions are so natural that the viewer almost forgets the gap in age.
In the same flick, Dunst/Marion has incredibly sexy chemistry with the 40ish Eddie Izzard, playing 35-year-old Charles Chaplin.
Least believable: Too many to name.
Clint Eastwood starred opposite Frances Fisher in the Unforgiven. I believe they were dating at the time. I was so impressed by the lack of an age gap; it was so refreshing to see a 60ish leading man not paired up with a chick in her twenties. Then I realized that Frances Fisher is over twenty years younger than Clint! There’s still a huge age gap; it just looks good compared to Woody Allen et al.