I'll often do it when on vacation and somewhat less frequently when at home on the weekend if having a nice brunch with friends. Never to start a work day, even if it's free. I can enjoy a drink or two with lunch, but if I hit it in the morning my focus just isn't there for the work day.
As far as the actual morning drinks go, I like bloody marys, but only the first few sips. Just too heavy for me to enjoy a whole glass. Mimosas are ok but I don't like all the sugar. Give me vodka with a nice tart grapefruit juice, or some sugar free red bull!