Hello!

Stand in circle

Round 1 - Hello! / Hello!
One person crosses the circle and greets 1 person by saying "hello" and shaking hands with them. This next person then crosses the circle and greets another person. (then add more people crossing)

Round 2 -  ... Goodbye, Goodbye + Hello!/Hello!
One person crosses circle and waits while the person they are choosing says goodbye to each of their neighbors (goodbye!..... goodbye!) and then greets them. This next person then crosses the circle to choose the next person. (then add more people crossing)

Round 3 - ....Goodbye, Goodbye, Hello!/ Hello! Hello! Hello!
As above except after the chosen person says goodbye to each neighbor the person who crossed the circle also says "hello" to each of the neighbors. ie. from player 1's perspective the choose someone, cross the circle, wait while player 2 says goodbye to each neighbor, says hello to player 2, then says hello to each neighbor.  (then add more people crossing) 

Variations -

Neighbors introduce
Player 2 introduces their neighbors to Player 1. Rather than Player 1 initiating the hellos to the neighbors of Player 2. 

Use names

Experiment with having people use names (or not) and how that impacts the experience. 

RELATED -

Bagel vs Croissant 
Jenny Drescher & Ellen Ornato shared about how they have groups form first a 'bagel' and then a 'croissant' shape and have a new person try to join the conversation when the group is formed in a circle (bagel) vs croissant (leaving an opening).  

Greetings
Have the group walk around, greeting each other and saying Hello and them moving to the next person. The facilitator gives instructions of HOW to say Hello. For example, like small children seeing each other in kindergarten at the start of the day, like strangers on a busy city street, like long lost friends, in a foreign language, like you don't trust them, late for a meeting, etc.