There are Team Challenges.
These are initiated by a team for a specific project through the BOINC Stats / BOINC BAM! site.
They last a finite amount of time each. Usually about a week.
They can be found here.
The link for each challenge will have other links showing ongoing and final stats for individual and team placement.
I try to keep up with the team challenges and post links to them at the forum page here.
To participate, you need to do two things:
1) Have an account with the project listed in the challenge making sure you have joined the team, "SETI.USA" for that project.
2) Crunch work units for that project during the dates listed for the challenge.
Credits you earn automatically get added to the team total.
You can also find your credits in the individual stats for the challenge.
On the same site are project challenges issued by the projects themselves.
I don't track these in the forum at the present time.
They are listed here.
Participation in these is the same as above.
Also there is an annual challenge/competition that our team participates in heavily.
It is the Pentathlon hosted by team SETI.Germany.
The home page showing last years info is here.
It runs for two weeks with 5 (hence pentathlon) overlapping events (projects).
To participate, you need to have a registered account for each of the 5 projects listed in the challenge for the current year.
You also need to have joined the team, "SETI.USA" in each of those project accounts.
Then crunch the project during the times it is active in the challenge.
We try to coordinate our team strategy in the members section of this forum to maximize our efforts in the event.
The Pentathlon is a blast and brings the team together.
Hope this helps a little.
Others may add to this if I've forgotten anything or misspoken.