This is a game you can play if you're talking about interesting experiences, achievements, or telling stories. Give the students a few minutes to write about something that they've experienced in the past. The examples I give them are: paragliding or bungee jumping, meeting their girlfriend or boyfriend, a special vacation, eating an interesting food, etc.
When the students are finished writing, have them put their names on the paper. Collect them. At this point, I'll usually put the students in teams of 2 or 3. Then, read the papers out loud to the class and have the students write down the name of the person they think it is. Exchange papers with another group, give answers and you have your winner.
This works well in my classes because even though there are about 20 people, they know each other well because they are all the same major and have all their classes together. If there are some students not of the same major who are repeating the class, I'll make sure to put them in a group with other students who know the majority of the students.
This could also work well for a smaller, more advanced level class of mixed-major students as a "get to know each other" kind of activity.