Sega manufactured games that late, but they didn't publish them. (Admittedly, they did continue publishing DC games - only in Japan - through 2004, which is still quite a while after the system was retired. The fact that most of those were easy ports from Sega's Dreamcast-plus-RAM arcade hardware is what made that happen, though; something which doesn't exist for PS3 or 360.)
According to Wikipedia
, which does cite a source, the last game that Sega published for the Dreamcast was in 2007.
The last Dreamcast games published by Sega of Japan were the 2007 releases Trigger Heart Exelica and Karous. Ending 9 years after the release of the console.
If you want to get even crazier, Square Soft is releasing a Final Fantasy XI expansion pack later next month for the Playstation 2
. No, that's not a typo. It's coming out for other systems too and it is just an expansion pack, but still that's quite impressive support.
Final Fantasy XI: Seekers of Adoulin