Final answer:
The Emmy-winning CBS show set in 2030 that ran from 2005 to 2014 is 'How I Met Your Mother'. It is known for its unique narrative structure and has received critical acclaim, including Emmy awards.
Step-by-step explanation:
The Emmy-winning CBS show that ran from 2005 to 2014 and was technically set in the year 2030 is How I Met Your Mother. The show is a comedy that starts in the future, with the main character, Ted Mosby, narrating to his children the events that led to him meeting their mother. The narrative unfolds through flashbacks starting from the year 2005. Over the course of the show, it received critical acclaim and several awards, including Emmys for aspects such as its cinematography and editing.