Since QuakeLive went public at the end of last February, the majority of the tournaments being held were about duel. But with the addition of private servers for organizers and more recently of a few "competition" features, it all became a lot easier for team-based matches. Now the TDM & CTF cups are growing in numbers since the beginning of summer:

ClanBase is currently running a TDM 4v4 Featured cup with cherubim, Reason-Gaming, d? and LowLandLions in the Division 1 semi-finals. And also a CTF 4v4 Summer cup which started directly on single elimination playoff.
Maplist: CTF - qzctf2, qzctf3, qzctf7, qzctf8, qzctf10 / TDM - qzdm6, qzdm7, qzdm14, qzdm20

ESL just published the groups for their CTF 4v4 and TDM 4v4 cups and are still accepting clans. It was initially planned to have a pro TDM and a TDM cup, but they're now holding a big pro TDM cup with 2 divisions. These will start very soon.
Maplist: CTF - qzctf2, qzctf3, qzctf7, qzctf8, qzctf10 / TDM - qzdm6, qzdm7, qzdm14, qzdm20, qzca2

Kuh3Liga is also having a Summer Cup 2009 with some TDM 4v4 action and the sign-ups are now closed. The 40 clans will play their first group match this very next Sunday.
Maplist: qzdm6,qzdm7,qzdm14,qzdm20

BiBs just finished their first CTF 5v5 season last Sunday with the victory of LowLandLions over versatile Gaming and seem in a good shape to have a 2nd season after this summer.
Maplist: qzctf2, qzctf3, qzctf7, qzctf8, qzctf10

Sources: ClanBase, ESL, Kuh3Liga, BiBs