Rail travel without a JR Pass

I live in Japan on a residency permit, and so do not qualify for a Rail Pass, unfortunately. I think that goes for the Hokkaido Rail Pass, too.

I have been asked to accompany some some friends from abroad on a 2 week trip to Hokkaido and Northern Honshu. They will be on rail passes, of course, and covering a lot of ground.

I winder if there are rail discounts or deals available to Japan residents, for unlimited travel in those areas?

There is the Hokkaido Free Kippu for Hokkaido:
http://www.japan-guide.com/e/e2357_001.html

And there are "free passes" for exploring the Tohoku Region for departure from and return to Tokyo.

Note also that if travel only in Hokkaido and Tohoku and arrange the order of your trip in an efficient way, the rail passes might not be that much cheaper than regular tickets. It could even be more expensive.

It is difficult to give specific advice without knowing the exact route.

If you live in Tokyo or the greater Tokyo Area, you could consider buying 'Gururi Hokkaido Free Kippu', or whole Hokkaido unlimited travel ticket with transport between Tokyo and Hokkaido either on the Tohoku Shinkansen or in the B-class sleeper berth in the overnight train 'Hokutosei'.

http://www.jnto.go.jp/syd/pdfs/TokyoSapporobyJR.pdf

Currently only one Hokutosei runs each way daily.
This is totally as mighty as the JR pass in Hokkaido and on the Tohoku Shinkansen. However the drawback of this ticket is that you can't make layovers on the Honshu island on this ticket, and the validity is only for 5 days, though if you take the Hokutosei on day 5, it's valid until you arrive at Ueno on day 6. You might consider concentrating on Hokkaido if you use this ticket.

--This is totally as ALMIGHTY as the JR pass--