From the OP’s title I thought that we were going to talk about Nick Cage’s Gone in 60 seconds during which the beautiful Eleanor was destroyed and I as a red blooded American male got something in my eye.
But no, we’re talking about other movies. I haven’t seen Brian’s Song but it sounds familiar, I may have read it or something.
Saving Private Ryan got something in my eye, most definitely.
I outright cried at Free Willy though.
Lou Gehrig Story (The “Speech” always chokes me up)
Field of Dreams
Schindler’s List (at the End)
Brian’s Song never did much for me.
When I was a kid, Dorothy’s very sad sounding “Somewhere over the Rainbow”
Oh, this is showing my geekdom. In Star Trek III when the Enterprise is destroyed. I teared up seeing it the first time in the theatre.
I can only think of 4 movies that made me weepy:
Titanic
Big Fish
Old Yeller
Turner and Hooch
I think any movie where a dog or a father dies has a good chance of making a man cry.
For me, the most tears were brought on by The Joy Luck Club. I remember sitting in the theater and hearing the clearing of throats and sniffles as the women began crying. I looked around and saw that most men were staring stoically at the screen. Then came the scene with … the babies. The waterworks started in earnest as the whole theater filled with the sounds of sniffling and weeping. Afterwards, in the men’s room, I was surrounded by men with red eyes and blotchy faces. No one wanted to make eye contact or even refer to the movie. Any conversation was a few mumbled testosterone laced references to sports… “How 'bout them Niners?”
No nominations for Rudy yet?
My SO had a lump in his throat during the romantic scene in The Last Samurai, when she’s dressing him.
Schindler’s List
Saving Private Ryan
Chariots of Fire (an uplifting sort of allergy attack)
Star Trek 2 when Kirk’s voice breaks while eulogizing Spock. Gets me every time.
Huh. A number of mentions for Old Yeller, but none for what I thought were the most obvious candidates – Shane and The Cowboys. These seem to me like the male version of the Lifetime movie, only instead of playing on the viewer’s fear of being supplanted in a domestic role, these movies play on the male anxienty about the loss of a father figure.
These did it for me:
O’l Yeller, of course.
My Dog Skip, which is just an updated O’l Yeller 
Spock’s seath scene in Star Trek II
The end of Schindler’s List
The last scenes of Empire of the Sun
Glory
The ending of The Killing Fields had quite a few men I know teary. And a number of them admit to an attack of tears during Boromir’s great death scene in Fellowship of the Ring .
Many great ones mentioned in this thread…
The English Patient
Where Ralph carries Kristin Scott-Thomas out of the cave. Couldn’t speak for some time after that.
and several bits of Eternal Sunshine. Got me thinking and blurred my vision on a couple of occassions. Gotta thank the dopers for the tip to watch this one.
SW Episode I had me close to tears but thats a different matter.
Bambi seriously bummed me out, but I was a youngling then.
Bridge to Terrabithia sent me into a 3-day funk after the tears dried, but… yeah, I was little.
Embarrasingly, Titanic worked on me as well.
On, and in high school, Death of a Salesman on VHS (was that Hoffman?) had me on the verge of tears.
I’ll second that.
FWIW, Keith Olbermann recently wrote a nice tribute to Moonlight Graham here
The Rookie. I didn’t expect it at all, and certainly not from a movie starring Dennis-freaking-Quaid, but the scene in which:
He calls his son from the road and says, “Your old man’s going to play in the majors!”
Had me a bit weepy.
Did they ever make a movie out of “Where the Red Fern Grows”?
I sobbed like a little girl when I read that book. Of course, I was a little girl, but still.
I can’t speak for men other than my husband, but I know that he got pretty teary with “Field of Dreams” and “My Dog Skip.”
“Suuuuppperrrmaaann!”
yes, i know it’s been named before, just adding my vote to the “got something in my eye” crowd
Brian’s song, but that was ages ago, not sure how I would hold up now. The scene in Patriot where the little girl chases after mel gets me big time.
It would also have to be the original James Cann/ Billy Dee Williams Brian’s Song. The recent Disney TV production was just lifeless.
Also, nobody (at least none of my kids) knows what “when you hit your knees” means anymore.
For Mr. Winnie:
1. Miracle
He weeps without mercy in two parts – when the coach points to the crowd chanting “U.S.A! U.S.A!” and says to the players “You hear that? That’s for you.” and of course when the announcer yells “Do you believe in miracles?” he just completely loses control. When we saw it in the theater at that point I heard male-sniffling all around me.
2. My Life
3. Saving Private Ryan
We had to go get drunk after that movie.
4. Rudy