Getting to know a little about your students the first day of class helps to make them feel more comfortable in the classroom with you and each other. Doing an icebreaker is a good way to involve the class and show that you expect them to participate in class activities. Some examples of icebreakers include:
Have students introduce themselves (you pick the categories such as name, major, home town, most unusual job held, favorite author, latest book read, thing they are most proud of, etc).
Put students in pairs and have them share info. Each person then introduces their partner to the rest of the class.
Give students a stick-on badge and have them write several descriptive terms about themselves. Then have the students find someone else in the room with similar descriptions and spend 2-3 minutes talking with that person.
Have each student introduce themselves by saying "I've done something no one in this class has done which is ..." If another student has done this, the student must find something else to share.
Put together a bingo card with various descriptors such as "has more than one major," "is from Chicago," "has a twin," etc. Have the students mingle to find others to sign their card in the appropriate boxes if they fit the descriptor.
Have students introduce themselves and tell how they got their name (could be nickname).
Put students in small teams of 4-5 people and have them develop a list of things they have in common. Have them share the most interesting things with the class.
Have a bag of trinkets including things like a pencil, spoon, gum, whiteout, string, lots of McDonald's kids toys, etc. Have each student pick something from the bag that represents their personality and share why as they introduce themselves.
Icebreakers can even be used in large classes. Charlotte D. Sutton (Auburn University) teaches Management classes with 400 students. She has them break into groups of 4-5 and introduce themselves and share phone numbers so that everyone knows others in the class. Then they have to identify the five most important things that a manager does. After they have done that, she goes through the class with a wireless microphone and get a representative of most of the teams to share what they thought. Another student writes all of this on the board. She says that when done, she basically has an outline of the class and is able to say, "Good, these are the things we are going to talk about during the course this semester."
Obviously icebreakers take time that first day of class but they are worth it in terms of establishing the classroom culture you want.