Take index cards and put various stickers on them to form groups. For example, if you have 21 students, make one pack of cards with animal stickers that put students in 7 groups of 3. Examples are 3 rhinos, 3 lions, 3 monkeys, etc. Shuffle the cards and walk around the room, allowing the students to pick a card. Let them look at it their cards, but they shouldn't show anyone. Then, give the directions for the activity. After that, the students should get up and WITHOUT talking find the others in their group. After they find each other they bring the cards to the teacher. Bundle all of the cards up with a rubber band, and make a top card to tell you that the set is for 7 groups of 3. You can make other sets for other group configurations, such as 5 groups of 4 (one group has 5). Once you make them up and label the cards, you can just pick which you want to use that day.

Randomly pass out UNO cards. You can have the students meet with people of the same number, the same color, or the same shape. Don't let them know in advance which you are going to choose, and they will be less likely to trade.

For partner activities, make a set of index cards with famous up to date pairs on them. Pass them out to the students and have them find their match. You can use names like Bert and Ernie, Fred and Wilma, Curious George and the Man with the Yellow Hat, Robinson Crusoe and Friday, etc. Update those who may become out of date each year and add popular ones to it. Also, have at least one threesome in case you have an odd number of pupils attending that day. You could include Larry, Mo, Curly, etc. for this. The kids love to see who they get and then have to do a little thinking to find their match. You can also use this for teacher inservices when you want the teachers to do an activity together. This allows them to work with someone different for a while.

For each group, create a puzzle with the same number of pieces as students to be in that group. Paste a picture on a sheet of tagboard an laminate it. Cut the pieces apart, use a permanent marker to mark the number of students in the group on the back of the pieces, and store them in a Ziploc baggie. When it is time for a group activity, give each student a puzzle piece. Then have them find the students with the rest of the puzzle.

While I was completing my student internship, my cooperating teacher used playing cards with students names on them to randomly call on students.  For a lesson one day, I realized that I didn't want the students to group themselves and I also didn't want just tell them who was going to make belong in a group.  So I just picked up the playing cards, shuffled, and dealt four cards.  Those students were in a group.  They actually liked this.  Of course not as much as them picking their own groups, but they completed their work in a timely and efficient matter and there were no feelings of animosity towards me.  It was great.