Final answer:
The show in question is 'How I Met Your Mother,' a sitcom that aired on CBS from 2005 to 2014 and is set in the future year 2030.
Step-by-step explanation:
The Emmy-winning CBS show that ran from 2005 to 2014, but was set in the year 2030, is How I Met Your Mother. This sitcom recounts the main character, Ted Mosby's, lengthy and elaborate story of how he met the mother of his children. The narrative framework is set in the future, where an older Ted, voiced by Bob Saget, narrates this story to his kids.