Decent list, but it suffers from a severe lack of Unforgiven. I know it's more about sheer brutality than making men cry, but Clint Eastwood is so compelling. He protests so often that his violent past is behind him, his wife changed him, all while pursuing two men and killing them for the bounty. After he and his compatriots murder the last man, he stoically admits that "Everyone has it coming," knowing that he can never be forgiven for what he has done. He deserves death just as much as the men he killed. And when he learns that the sheriff has killed his friend, he goes full-on psychopath, slaughtering a roomfull of deputies and threatening to burn down the entire town. His longing for redemption has only resulted in the death of his friend and his return to a state of unforgivable violence. It is easily the best western I've ever seen, and has such a tragic final act that I can't help but shed a tear.
You've got to include Once Upon a Time in the West, don't you? Even putting the emotional revenge story aside, the whole thing just gives you such a feel for the people involved in building the frontier: it's rare that by the end of any movie you have developed a compassion for everyone including the villains.
I'd say that Unforgiven is more about being bleak and nihilistic than it is about being a "crier" of a Western. But what about the Magnificent Seven? Getting together one of the biggest groups of hollywood badasses in one film then killing off more than half of them? That doesn't make men cry?
I suppose that's not fair... it didn't make me cry, but neither did Tombstone.