A couple more stand-by games that I'm sure that everyone already knows, but just in case (and also because a reminder is always handy!) It may be that I have already added these but I just skimmed over them when I went looking to see what was missing!
1) 20 questions.
I have already commented that I believe we don't give students anywhere near enough opportunities to practice asking questions - we tend to focus on getting answers from them. 20 questions is great for getting students to ask questions & think a bit laterally - even though it does focus on yes / no questions. I'm sure that the instructions for playing 20 questions are already online in a million places - let me know if you think it is worth adding them here.
2) Celebrity heads
Stick a sticky label on each student's back with the name of someone they all recognise - a celebrity, sports star, a well known TV / film character, even a teacher from your school. (it's best if the sticky labels are pre-prepared!) Students need to ask questions (again, often this is confined to yes / no questions) to work out who they are. In schools, celebrity heads is often played by seating 3 or 4 kids at the front of the class with the celebrity names written above and behind them - but this means just those 3 or 4 students get the practice asking questions. By putting a different name on each student's back, everyone is involved. I generally have some extra labels pre-prepared just in case anyone guesses super-fast. It can be great to get students to nominate celebrity names also - but you may need to vet them first.
There is some specialist vocabulary required (such as various careers) but this can be given out & often comes in handy when the students are talking about themselves or needing to describe others anyway. :)
I have occasionally used students' names as part of the mix for this game, but you need to know your students well to make sure that there won't be any hurt feelings. Putting a student's own name on their back can be fun too after you've played it a couple of times...