Begging With a Purpose
"I just need a few more dollars for the bus," at the bus station, or "I just need $5 to get some gas," at a gas station. There's also a variation where you will be presented with a reward: "I just need money for a cab to get uptown, but I'll give you sports tickets/money/a date/a priceless vase."
Gas Pump Scam
Someone will offer to pump your gas or hang up the pump for you when you're finished. They will pretend to do so but instead will sell gas at a discount for cash to people that pull up after you leave, while your card is still being charged.
Three Card Monte, Also Known As The Shell Game
Unbeatable. The people you see winning are in on the scam.
Drop and Break
You bump into someone and they drop their phone/glasses/fancy bottle of wine/priceless vase and demand you pay them back. In reality, it's a $2 pair of reading glasses/bottle of three-buck-chuck/tasteful but affordable vase.
CD Sales
You're handed a free CD so you can check out the artist's music. They then ask for your name and immediately write it on the CD. Once they've signed your name, they ask you for money, saying they can't give it to someone else now. Often they use dry erase markers, or cheap CD sleeves. Never use any type of storage device given to you by a random person, as the device can contain malware.
White Van Speaker Scam
You're approached and offered speakers/leather jackets/other luxury goods at a discount. The scammer will have an excuse as to why the price is so low. After you buy them, you'll discover that they are worthless.
iPhone Street Sale
You're approached and shown an iPhone for sale, coming in the box, but it's open and you can see the phone. If you buy the phone, you'll get an iPhone box with no iPhone, just some stones or cheap metal in it to weigh it down.
Buddhist Monk Pendant
A monk in traditional garb approaches you, hands you a gold trinket, and asks for a donation. He holds either a notebook with names and amounts of donation (usually everyone else has donated $5+), or a leaflet with generic info. This is fairly common in NYC, and these guys get aggressive quickly.
Friendship Bracelet Scam
More common in western Europe, you're approached by someone selling bracelets. They quickly wrap a loop of fabric around your finger and pull it tight, starting to quickly weave a bracelet. The only way to (easily) get it off your hand is to pay.
Leftover sales
This scam involves many different items, but the idea is usually the same: you are approached by someone who claims to have a large amount of excess inventory and offers to sell it to you at a great price. The scammer actually has low quality items and will lie to you about the price/origin of the items.
Dent repair scams
Scammers will approach you in public about a dent in your car and offer to fix it for a low price. Often they will claim that they are mechanics. They will not fix the dent in your car, but they will apply large amounts of wax or other substances to hide the dent while they claim that the substance requires time to harden.
Gold ring/jewelry/valuable item scam
A scammer will "find" a gold ring or other valuable item and offers to sell it to you. The item is fake and you will never see the scammer again.
Distraction Scam
One person will approach you and distract you, while their accomplice picks your pockets. The distraction can take many forms, but if you are a tourist and are approached in public, watch closely for people getting close to you.