Nope, they are supposed to be emotionless rock boulders.
Seriously, guys.
Any psychologist can confirm that showing emotions is requires strength, and is not necessarily a weakness, considering the person being well tempered in it and true to themselves, and that it often takes courage.
It is okay for men to cry, and bravely so.

It could be a sign of weakness, unmanliness and cowardice in certain situations, though, but that's not the kind of crying that I'm talking about and the kind of tears a godly man will have shed. I go with what the Bible says is okay:
Reactions to extreme and tragic situations, great spiritual distress, repentance:
Genesis 27:38 And Esau said unto his father, Hast thou but one blessing, my father? bless me, even me also, O my father. And Esau lifted up his voice, and wept.
Psalms 6:6 I am weary with my groaning; all the night make I my bed to swim; I water my couch with my tears.
2 Kings 20:5 Turn again, and tell Hezekiah the captain of my people, Thus saith the LORD, the God of David thy father, I have heard thy prayer, I have seen thy tears: behold, I will heal thee: on the third day thou shalt go up unto the house of the LORD.
Job 16:20 My friends scorn me: but mine eye poureth out tears unto God.
Psalms 56:8 Thou tellest my wanderings: put thou my tears into thy bottle: are they not in thy book?
David seems to have cried quite a lot!
Deep occasions of expressing love (or mourning), either towards family members, closest friends, or a spouse:
Genesis 29:11 And Jacob kissed Rachel, and lifted up his voice, and wept.
Genesis 33:4 And Esau ran to meet him, and embraced him, and fell on his neck, and kissed him: and they wept.
Genesis 37:35 And all his sons and all his daughters rose up to comfort him; but he refused to be comforted; and he said, For I will go down into the grave unto my son mourning. Thus his father wept for him.
Genesis 43:30 And Joseph made haste; for his bowels did yearn upon his brother: and he sought where to weep; and he entered into his chamber, and wept there.
1 Samuel 20:41 And as soon as the lad was gone, David arose out of a place toward the south, and fell on his face to the ground, and bowed himself three times: and they (David and Jonathan) kissed one another, and wept one with another, until David exceeded.