Originally "v" stood for "victory." Nowadays, it's used as the "peace sign." You see it often when people are trying to invoke hippies, and it's such an iconic part of taking photos in Japanese culture that Time Magazine did a write-up on where it came from.
However, make sure you have your palm facing away from you. In Australia and the UK, this sign (with the palm facing inward) has had the same meaning as the middle finger since at least the year 1330. In those countries, you'll be saying "F*** You!" which is quite the opposite of "peace."
Making a circle with your thumb and pointer finger usually means "OK!" in the U.S. In some Middle Eastern countries, it represents the evil eye. A more widespread meaning, though, is "you're an a**hole." It's taken this way in Greece, Spain, and Brazil.
There's an extra layer of homophobic subtext to the gesture in Turkey. Nixon once famously made this his first impression to an entire country. Don't do the same. Even in the U.S., white nationalists have recently co-opted the symbol for their own uses, warping the seemingly harmless original meaning depending on the context in which it is presented.
You might use this gesture to delicately wave off someone's offer of a drink refill or to tell someone to stop when they're parallel parking. But in Greece, Africa, and Pakistan, this gesture represents you rubbing someone's face in excrement. That seems like a really specific thing to have a hand gesture for, but who are we to judge a good insult?
This gesture has also taken on some aggressive sexual connotations in recent years. For those who don't agree with the #MeToo movement, it's meaning is in essence a defiance of the meaning "stop."
This gesture doesn't mean anything in particular in the U.S., which is just as well, because it has riot-causing potential elsewhere. If you group the fingers of your right hand together, while pointing to them with your left, you're telling someone that they "have five fathers"—in short, you're calling them a bastard. This one is particularly egregious in most Arab countries and in the Caribbean. You're not as likely to do this one on accident, but given the intensity with which it's received, it's only fair that you know about it from the outset.
To an American, crossing your fingers is a slightly cheesy way to invoke good luck. No one really does it outside of female leads in tone-deaf romantic comedies, but the meaning is still understood. In Vietnam, however, the gesture is believed to have an...explicitly feminine appearance. Consider it a female analogue to flipping someone off.
Hands Below the Table
It's drilled into American children not to rest their arms on the table when they're eating. But in France, the polite thing is to keep your hands on the table, palm down, on either side of your plate. When your hands disappear below the table, your host will be wondering what exactly it is you're doing with them.
Sign of the Horns
In America, this gesture generally means that you take your Texas roots a little too seriously. Depending on thumb placement, you might also identify yourself as a metalhead. In Brazil and Venezuela, this gesture is a wish for good luck. For people in Italy and Spain however, this means their spouse is cheating on them. Furthermore, in Portugal, Colombia, and Brazil, this gesture means "your wife is unfaithful," often with the corollary, "and you're too stupid to realize it."
Using Your Left Hand
This one's rough. There are still places in the U.S. where people are given a hard time for using their left hand, but in large swaths of Africa, Asia, and the Middle East, the left hand is still mired traditionally with connotations of personal hygiene. To give a gift with the hand that's traditionally used for toilet paper is a big no-no, as is using it to eat. Also, it's not recommended to go for the handshake.
This gesture, a closed fist with your thumb between the first two fingers, is usually only seen when your uncle or grandmother has "got your nose." Unfortunately, it's heinously offensive in large portions of the world. Turkey, Russia, and Indonesia will read it as a big "screw you!" In some countries, especially Italian-speaking ones, the gesture is seen as being evocatively feminine, in much the same sense as crossed fingers in Vietnam.
If you want to look fancy (or at least pretend to look fancy) when drinking tea, you might pop your pinky up as a little flair of refinement. But in China, this gesture is a real downer--it's basically the equivalent to an American thumbs down. If you see this gesture there, the person you're speaking to is clearly not happy about something.
"Come Here" Finger
When you beckon someone with your index finger in America, it could mean a few things--you might use it to look seductive to a partner, or a parent might use it on a misbehaving child. But in the Philippines, this gesture is an absolute no-go. This gesture is only used to call dogs, and if you try it on a person, you might end up getting arrested!
The "Italian" Gesture
Smelly Hand Wave
Animal Horns on Head
Pointing at Someone
For a long time, pointing at someone could be considered a semi-aggressive gesture in the USA, but over time, it's also come to be a humorous sign of approval. However, in countries across the globe this gesture is considered especially offensive. For example, in some African countries, it's only appropriate to point at objects, never people.
Handshakes are a tricky thing in the United States. A firm shake is a sign of respect, but if you squeeze too hard, you're likely to be considered aggressive or arrogant. In Japan, the bar is much lower for what counts as "too hard." What many Americans would consider a polite, firm handshake would be seen as overkill there.
In the USA, if we want to insult someone, we might flip them the bird. The middle finger in our culture is seen as one of the most disrespectful gestures you can use. However, don't get offended if you find yourself in a sea of middle fingers in China--it's the digit they normally use to point with and conveys no ill will.