A plug-in like Cimy User Extra Fields allows you to attach custom meta fields to users. You could set up a text field called "Team" for your users, then you can run a custom query against that field to present a list of members of each team on a custom page.
There's also a plug-in called User Access Manager that allows you to set up explicit groups of members.
I haven't used either plug-in, so while I can't personally vouch for their usability, they do come highly recommended from some of my colleagues.
Update
There's also a plug-in I wrote some time ago called RegLevel. It was used at the time create separate user groups for Affiliate sales by a specific client, though I've spoken with people who have used it in other ways as well. If you pair it with a role management plug-in (like Role Scoper), you can create custom "Roles" with custom titles.
So a specific use case:
- Copy the "Subscriber" role and create a "Team 1" role a "Team 2" role and a "Team 3" role
- Use RegLevel to create custom registration URLs for each team
Anyone who uses, say, http://blog.url/?reglevel=team1 to create an account will automatically be assinged to the Team 1 role. If anyone signs up as a regular user, you can easily move them from the Subscriber role to the Team 1 role.