Find Someone Who... A great resource to use as an ice breaker; ideal for a new tutor group. This encourages students to get up and about communicating with others to extract information and find things in common, breaking the ice and begin bonding with one another! TES Teaching Resources
The Pipecleaner (aka "Fuzzy Sticks") Challenge is one of my favorite STEM activities to introduce students to STEM learning. This is a fun, inexpensive, and engaging challenge that can be tailored to different ages, settings, and time-frames. This challenge is also an excellent team icebreaker.
This website has lots of ideas for icebreakers. It has games for different size groups (i.e., 2-3 people, 5-7 people, etc.) There are get-to-know-you games, and team-building games that would be very useful in the classroom.