A Japanese research team filmed a live giant squid (although it died while it was being caught):

The research team, led by Tsunemi Kubodera, videotaped the giant squid at the surface as they captured it off the Ogasawara Islands south of Tokyo, earlier this month. The squid, which measured about seven metres long, died while it was being caught.

"We believe this is the first time anyone has successfully filmed a giant squid that was alive," said Kubodera, a researcher with Japan's National Science Museum. "Now that we know where to find them, we think we can be more successful at studying them in the future."

Link | See also: Video at Reuters | CNN