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.
Wikipedia said:The last Dreamcast games published by Sega of Japan were the 2007 releases Trigger Heart Exelica and Karous.[5] 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