I'm taking the opportunity now to expand my ideas a bit...
Part 1 - Communication Game
Learning should be fun, but it's all too easy for fun to become a higher priority than learning. Especially when we start out, we can think that the nuts and bolts of grammar - let alone spelling, paragraphing or register - are 'boring,' and 'too difficult' for our students. We want them to like us and enjoy the lessons, so consciously or otherwise, we skimp on the boring stuff, and pile on the fun. The result? Unchallenged, unmotivated students who are poorly prepared for using English in the real world, and may even end up complaining about our teaching style. "So and so's classes are fun, but I need to improve my English."
It's not that games are bad, but they do need to have a clear purpose - and some students will need to understand that purpose before they see any value in the game. So, what are some valid purposes?
First, the Warmer - for the beginning of the term, to help a new class to gel.
Everyone has their favourites, and one of mine is the Number Game. Every student thinks of a number that has some personal significance to them (try to steer them away from just choosing their age as it's so obvious). It might be their house number, their lucky number, the year their country got independence, or anything really. In small groups, students tell their numbers, and the group has to guess the reason. This game is good for giving students practice in asking questions and speculating (you could use it to gauge current ability before a relevant grammar lesson), and also because the students have totally free choice over what personal information they reveal, so it is less pressurised for them in a new class situation.
Next, games can be focused around producing particular Target Language.
A great example for this is the Blindfold Obstacle Course. A student is blindfolded, then the class and teacher arrange an obstacle course for them, using whatever is available in the room (pieces of paper on the floor that they must avoid treading on would be a minimalist version). The class then has to direct the blindfolded student on a particular route through the room. To avoid the louder students monopolising the directions, you could have a rule that each class member can only speak once, then has to wait their turn till everyone has given one direction.
This game of course practises the imperative and vocabulary for direction, but also could be used for prepositions (crawl under the tablecloth), phrasal verbs (pick up the hoop) and speaking with precision (shuffle forwards 3 inches, then turn 90 degrees to your left).
Another valid purpose for games is to enhance students' Confidence.
If you have a class with one or more very quiet students, try a Shouted Dictation. Divide the class so that half are at each end of the classroom, facing the opposite group. Each student is then paired with the one opposite them. One group are the readers, the other group are the writers. You then need to give each reader a different short text to read, which they have to dictate to their partner. If you want to make it more difficult, you can play music, or radio static if you're feeling really mean!
The readers are dictating different texts simultaneously, so it gets loud pretty quickly. The writers have to accurately transcribe the entire passage (including punctuation), so they will start shouting too, asking for repetition, spelling, and clarification. I have done this activity with a class which included a nearly inaudible student, and the results were impressive. For more confident students it can also be very beneficial in terms of pronunciation and clarity.
The activity above is helpful for students who feel underconfident in the classroom. However, sometimes there is the opposite problem: the classroom is too safe. Students produce language happily in front of their teacher and classmates, but freeze up in a shop, at work, or in a speaking test. So sometimes we need activities to help students Produce Language Under Stress, strange though that may sound.
For this, I like to use two Backwards Interview games. The first one is based on a classic Two Ronnies sketch:
The second interview game is loosely based on the quiz show Jeopardy. Time A gives B an answer, which B has to think of a question for. Then B gives C an answer, C responds with a matching question, and so on. This is another game that's useful for practising question forms, and it can lead to some lively debate about whether a particular question and answer really go together.
Of course these are by no means the only possible learning purposes for games, but I hope that they are useful as examples. Please do comment if you would like to add any more game purposes for the EFL classroom, or suggest any tried and tested games.