As of March 26th 2016, Hokkaido will be connected to mainland Japan by Shinkansen. Reducing travel time between Tokyo and Sapporo by more than 2 hours. The Shinkansen line will run from Tokyo to Shin-Hakodate. Future expansion of the Hokkaido Shinkansen is planned for travel to Sapporo by 2030.

JR Pass validity on the Hokkaido Shinkansen:

The JR Pass is valid on all Shinkansen services on the Hokkaido Shinkansen, including the super fast Hayabusa Shinkansen. The value of the JR Pass is outstanding on this route, as a normal ticket would cost 22,690yen for one way.

Using regional passes on the Hokkaido Shinkansen.

The JR-East south Hokkaido pass is the only regional pass that covers the Hokkaido Shinkansen. This is unlike the Hokkaido Rail Pass which is valid for all trains around Hokkaido, with the exception of the Shinkansen trains.

Schedule:

There will be 10 E5/H5 Hayabusa services in each direction per day, between Tokyo and Shin-Hakodate at launch. Each train carries 731 seats, so there is plenty of room.

Passengers going to Sapporo can make a transfer at Shin-Hakodate to the conventional railways and use the Limited Express Super Hakucho to Sapporo.

Good to know:

-The Hayabusa train is fully reserved, meaning that a seat reservation has to be made in advance before boarding the train. Seat reservations are free of charge with the Japan Rail Pass.
-The Hokkaido Shinkansen has some of the best Green Class (First Class) carriages in Japan. It is worth considering upgrading the JR Pass to Green Class on this route, as it is still a long trip. Complimentary drinks, such as coffee, tea, water in addition to oshibori (hand cleaning towels) are served in Green cars as well.
-When searching with Hyperdia, leave the option: NOZOMI / MIZUHO /
HAYABUSA (SHINKANSEN) on. As the Hayabusa train is covered by the JR Pass.

Resources:
 English Timetable
Japanese Timetable
Recommended Tohoku and Hokkaido itinerary