[patio11]

For the benefit of HNers thinking they might want to visit Japan someday:

There are basically only two discounts for the shinkansen -- one is multi-trip tickets (回数券 -- which are mostly for businesses).

The other is something which is half a discount and half just outright subsidization of policy goals, the JR Rail Pass. It is a special ticket, only available to people who are visiting Japan and don't hold either a Japanese passport or mid/long-term visa, which gets you all-you-can-eat access to all of the JR lines (including the shinkansen, less one class of them). The cost for a week-long pass is less than that of a roundtrip ticket from Tokyo to Kyoto.

If you ever come to Japan, make sure you buy a voucher for one of these before you leave home, since they're not sold here.

[SoftwareMaven]

Many countries/regions have similar passes. I've used both BritRail and EuroRail passes in a similar way. Very much worth looking into; I got to see Scotland on a result.

[ekianjo]

Good point, but I was mentioning the discounts from a Local person point of view.