I've heard this called many things, but basically you get half the class to stand in a circle in the centre of the room facing outwards. Then the other half of the class form a circle round them, facing inwards. You shout a question and give them 1-2 minutes to discuss. Then the outer circle students take a step to the left (the inner circle doesn't move) and find a new partner. Repeat. Or you could just let them find out as much as possible about each partner, without you shouting questions.
Pick a question
You need a pack of cards and a copy of the question sheet here for each group of 3-5 students. Students take a card, and answer the question which it corresponds to. For example, the King of Spades is "What was your favourite toy when you were a child?". A higher level class could write their own questions (one group writes Qs for hearts, another for diamonds and so on, and then you combine the questions).
True or false
Write 5 sentences about yourself on the board, some true, some false. Students ask you questions and guess which ones are false. Then they write their own sentences and show to the other students who, again, guess if they are true or false.
Draw a star on the board. At each point, write the answers to questions. Then the students guess what the questions might be (for example 'rat' could be "what are your favourite animals?" or "what are you frightened of?"). Then students make their own stars and guess each other's questions.
Find someone who ...
There's lots of these ready prepared out there, but students can make their own. Give each student 5 slips of paper and get them to write 5 sentences about themselves on them. Collect the sentences in a hat, then hand out five to each student. Then they must "find someone who" the sentence is true for. It doesn't matter if they get their own sentence - then they should find someone who is the same as them!!!
Find something in common
This is very straightforward. In small groups (pairs or threes) students have to find as many things as possible in common. You could give them topics to help them, such as "family, hobbies, likes/hates, home, holidays, work". In feedback you might want to reinforce the use of "both/all of us" and "neither/none of us" to report the answers.