I don't think you see this too much today, but you may see it a lot in old westerns and high society social clubs.

Totally sexy when guys do this. It's kind of a reminder of the good old days when guys would remove their hats when being introduced to a woman. I love old fashioned manners.

Like a couple have already mentioned; this seems a relic of the past that went out with fedoras and Irish tweed caps. However, it was fairly common up until the guys my grandfather's age started to pass on. It had a certain gentle friendliness about it that I remember fondly - not unlike my grandfather himself.

Not as common as it used to be. Not too many guys wear hats anymore, except ballcaps, and I don't see to much of this anymore. The exception would be men who wear cowboy hats and it's usually followed by Ma'am.

I guess what I do would be considered a variant of this, for those who I'm familiar with; typically, I make an upwards nod, verbal acknowledgement, sometimes a hug depending on my mood. Not suggested for formal or professional occasions.