Group testing is very popular. It seems to me, though, that it has very little impact on grades, either positive or negative. In Elementary Statistics I have a component consisting of four small projects, including in-class oral presentations. These are supposed to be group efforts, but it often seems to be the presenter who does the work. Using cooperative learning on quizzes and exams has been quite successful this semester.
Students take an individual exam first, submit it, then retake it as a group.
On tests, items like these were used to assess individuals understanding of the group solved quiz problems. Since groups work at different paces, either trivial or somewhat hard problem solving in class are not as motivating to students. They get partial credit when their group solutions are better than their individual effort. Class evaluations indicate they think this is the most helpful type of group activity. I personally dislike having some groups done with an activity waiting for others to finish, so I have relatively short, group, think, interludes in class brainstorming times.