There is a day train option:
From Tokyo, take a hayate train on the JR Tohoku Shinkansen to its terminus in Hachinohe (3 hours). Then, take the JR Hakucho limited express to Hakodate (3 hours) and finally the JR Hokuto limited express to Sapporo (3.5 hours).
The entire one way trip costs around 22,500 yen and takes between ten and eleven hours. It is fully covered by the Japan Rail Pass. Note that seat reservations are mandatory on the hayate shinkansen between Tokyo and Hachinohe.
*Budget travelers with lots of time may consider the seasonally available Hokkaido & Higashinihon Pass for the trip.

and a night train option:

One or two night trains (more during peak seasons) operate daily between Tokyo's Ueno Station and Sapporo in each direction. Note that the Japan Rail Pass does not cover the expense for a berth (from around 6000 yen), the limited express fee (about 3000 yen) and a supplement for partially using non-JR tracks (about 3000 yen) on night trains between Tokyo and Sapporo.

http://www.japan-guide.com/e/e2356.html - has more info on night trains
Source(s):
http://www.japan-guide.com/e/e5306.html


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