Complicated problem + people to work on it = problem solved + team built
A group of people who work for the same boss is not a team.
Bosses need their people to be a team so that interdependent work doesn't fall between the Grey Gaps; and so work doesn't sit in the post room when the person it's addressed to goes sick or on holiday.
[Many] bosses invest in Team Building events because they think it will Build Team. It won't.
Playing a game which has no purpose other than the playing of the game creates conditions for people to be social with each other. To be fair this is a necessary precursor to asking people to do thing: it's easier to ask someone for something if you know their name. Its even easier if you know they live miles away and may have had a horrid commute because you can ask about their journey before you crack on with your request. Games like this are useful ice breakers but don't go and spend thousands on doing them for several days.
Social is not sufficient. Playing a game that is just a game doesn't allow the kind of richness of interaction which builds trust, creativity, shared ideas, synergy, interest, an understanding of the unique talents and enthusiasms of each person. To do that you need people to work on something meaningful which builds social, AND brings richness. And the way to do that is facilitate them to solve a complex or complicated problem together and then help them reflect on that experience to make what they have done re-usable.
You can use special games for this. Games which are specially designed to create the conditions for people to work together to solve business problems. They're called Serious Games and there are some great ones about. I use them to create conditions for teams to learn how to solve particular kinds of problems whether that's cultural or business improvement thats needed. A secondary output is of these is team building but thats rarely my primary reason for selecting a Serious Game.
If you want to Build Team facilitate them to solve a real problem which is holding your business hostage: whats the problem? what do we do about it? why, if we do that thing, do we say it will solve our problem? will doing it cause any new problems? can we live with those new problems or do we have to add something to our solution? how do we implement our solution? etc etc.
This year I've facilitated several, great groups of people to solve real problems holding their organisations hostage, and in the process we've created conditions for Teams to be Built. And High Performing Teams at that. Loving it.