During the Credits
There is a special thanks from Bungie at the start of the credits, but no extra scenes during the credits of Halo 3.
After the Credits (spoilers)
Similar to Halo 2, there are extra scenes shown after the credits of Halo 3 when beating the game on legendary mode. The extra scenes show Cortina asking if Master Chief can hear her, he’s then shown floating in space asking what happened. She explains that he made it through the portal just before it collapsed. Master Chief is shown going to sleep in a pod and telling Cortina to wake him if she needs him.
The second extra scene ends when their ship is shown floating towards a mysterious dark planet with a blue light shining behind it and eerie music playing in the background. Many believe that the planet is Onyx, the site of a major archaeological survey being conducted by ONI from the book Ghosts of Onyx included in the Halo novel series.
Update: The planet has been confirmed as the Forerunner planet, Requiem, which will be where Halo 4 will take place.