Time to turn to Mr. Bond. We all know the classic order, "Dry vodka martini shaken not stirred." If you order this I commend you...if you know what you are talking about. So, let's look at the meaning behind Bond's famous drink and then we can explore drinks in general.
A martini is a classic cocktail. Typically they are made from a combination of gin and vermouth and garnished with either an olive or a lemon (Its a Gibson if garnished with an onion). However, a trend began of replacing the gin with vodka since some do not take to the juniper berry taste of gin. This became widely popular and resulted in the majority of martinis being made with vodka. However, a well trained bartender will consider an order of "martini" to mean the classic version. Thus Bond stipulates that he wants the vodka version. Dry or wet refers to the amount of vermouth present in the drink. Some often praise only waving the cork over the glass as the proper amount of vermouth. By indicating "dry" Bond shows that he does not want a lot of vermouth. Martinis are prepared either by shaking with ice, thus cooling the drink, or stirred in the glass, thus keeping it at room temperature. Bond prefers cooled. If you know what it all means, by all means try it, but you run the risk of looking like a follower if you can't explain what you're drinking and why.
So, what should you drink?
The Classics - This group of cocktails hail back to the time of the speakeasy and always exhibit a touch of class. They are acceptable before or after a meal, never during, or just at a nice bar or club. They tend to be strong so exercise caution. This group includes: martinis, mahanttans, gin and tonic, tom collins, mint julep (reserve for hot afternoons or outdoor settings), and a couple of others.
The Questionables - These are a couple of drinks which have something of a stigma attached. The Screwdriver (vodka and orange juice) and other combinations of vodka and juice/soft drink tend to say that you do not like the flavor of liquor, only the effects, or that you are just trying to hide the booze in an innocent orange juice. Exercise caution this can make you look bad. The Bloody Mary is another danger. Not that the drink is bad or in any way wrong, but it comes with a recovering hangover/booze for breakfast stereotype.
The Not Alloweds - If it ends in "-tini" without the word "mar-" before it, no. Just no. Be wary of gimmick drinks and "house recipes." No car bombs, sake bombs, or the like. These give the impression that you just want to get tanked. Not a good image for a gent. Also avoid umbrellas and excessively fruity drinks. The exception to this is on the beach or a boat. Then the pina colada and daquiri are acceptable. Nothing with sex, navel, or drunk in the name. Again bad impression. Know your location. In the States margaritas with Mexican is acceptable (on the rocks, no slushies please), but in Mexico the margarita is seen as feminine and typically reserved for women and gay men. Just always be aware of the image you want to present.
The Straights - Any straight liquor is included. Scotch, bourbon, and blends are seen as high class. Order these neat, on the rocks, with water, or with soda per your tastes. Never just say the name of the alcohol. Tequila and whiskey move down the line. These are party or sorrow drinks. Use caution, but acceptable in the right circumstances. Finally, vodka. Vodka shots tend to say wasted, exercise caution.
Wine - Wine is a dinner and event drink. Avoid ordering it at a bar, unless it is a wine bar. Brush up on varietals and know how to pick a good wine. If not trust your sommelier.
Beer - Another dinner and event drink. Acceptable at very casual parties. Craft beer is great with a variety of foods. Saisons make a particularly nice match with Asian food and IPAs pair well with spicy food, both of which can suffer with wine. Do a little research before and trip and know the local brew and favorites. It will impress the locals and avoid any unpleasant jokes.
Always use caution with drinking and make sure your host and guests are comfortable with it. Never allow alcohol to put you or others in any danger. Finally, never allow a quick drink to give you a long lasting reputation.