Expressway passes are similar to other kinds of public transportation tourist passes(eg. JR Rail Pass) but for rental car drivers. You get unlimited uses of national or regional expressways without paying for individual toll gates, at a certain daily price. The more you spend time on the roads, the more you save. So just like rail passes, it's not definite savings, and is wholly dependent on your itinerary and travel route. Personally, I rarely use these, instead plan on traveling on regular non-tolled highways and regular roads as much as possible, which isn't without it's drawbacks, the main one being the speed limit is much slower on regular roads.
Do note: These expressway passes depend on also renting an ETC card, to put in the onboard ETC machine. ETC = Electronic Toll Collection. Almost all rental cars come with the ETC machine, but the card usually has a low cost daily rental fee(what i normally see is around 320yen daily). The ToCoo plan below, the Expressway Pass cost should include the ETC, but if you aren't using that package, you'll need to rent the ETC card separately via your car rental branch. (eg. Here's ETC rental info from Times Rental)
Japan Expressway Pass http://global.w-nexco.co.jp/en/jep/ or http://www.driveplaza.com/trip/drawari/japan_expass/
Kansai Expressway Pass http://global.w-nexco.co.jp/en/ksep/ (Service period:October 25th (Wed.), 2017 - December 17(Sun.), 2017)
Kyushu Expressway Pass http://global.w-nexco.co.jp/en/kep/
San'in-Setouchi-Shikoku Expressway Pass http://global.w-nexco.co.jp/en/sep/
Hokkaido Expressway Pass http://www.driveplaza.com/trip/drawari/hokkaido_expass/en.html
Tohoku Expressway Pass http://www.driveplaza.com/trip/drawari/tep2015/
Central Nippon Expressway Pass http://hayatabi.c-nexco.co.jp/cep/en/
ToCoo! Expressway Pass Plan https://www2.tocoo.jp/en/campaign/index?campaign_id=963