www.hyperdia.com comes in English and has all times local and national, including private lines, Shinkansen and, bizarrely enough, some airplane routes. Prices are quoted for one-way, return and commuter pass.
They also have some cool features for use with iPhone/iPad, including a voice command system (which sounds more trouble than it's worth). Those using an Android phone are offered a pretty swish mobile route finder which uses GPS.
Another popular option is http://www.jorudan.co.jp/english which is pretty much the same, but much more attractive. You can also book hotels and see maps of station locations through the results page. They also have various non-free versions of the site which add weather, tourism and offline features.
Alternatively you can use the fairly basic (Japanese) options of transit.yahoo.co.jp or transit.msn.co.jp.
Tips or advice in the comments please.