Swiss pass: Continuous or flexipass

Everyday you use the Flexi Pass counts as a pass day if you specify it. Between the first and last travel days, it gets a 50% discount on Swiss trains, but I doubt if it includes the mountain railways, since you only get a 50% discount on designated Pass days.

With a flexipass, on days you designate as pass days, you get full coverage of transit, except for lifts above Muerren (to the Schilthorn) and Wengen (to the Junfrau). The ride to the Schilthorn is 50% off, and the ride to the Jungfrau is 25% off. On days in between your first and your last designated pass days, the flexipass it acts as a half-fare card (including on these rides). So, there is no advantage to using a pass day when you are taking the high mountain lifts, as it's the same (Schilthorn) or cheaper (Jungfrau) to use it as a half-fare card and not use a pass day.

If you are going to other places, note that the same issue applies to some other lifts, like the one to Mt. Pilatus (half off with a pass day, half off with an "in between" day on the pass, so don't use up a pass day for this).

If you want it to act as a museum card, that uses a pass day. And once you've used your last pass day, the pass is "finished" even if you still have time left. In other words, if you get a 3 days in one month flexipass, and use a pass day on day 1, day 4, and day 5, it doesn't matter that you still have 25 days left in the month; you get no further value from the pass.

Harold's description is correct (but Sam's makes a wrong assumption). See also our Swiss rail page. The Swiss Pass for 8 continuous days costs about $400 per adult and covers trains, buses, city trams, boats, museums, and mountain rides as far up as Muerren, Wengen, or Grindelwald, for instance. It gives you a lot of hop-on convenience until you get to the higher mountain rides. A flexi pass gives you the same "fuller" coverage on a few of your longer travel days (about $265 per person for 3 days within a month or $320 for 4 days), plus gives you the option to buy all transport tickets (not museums) for half price on the in-between days (except still just 25% off Wengen-Jungfrajoch).

Laura's right, there is a discount for two or more adults traveling together on the Swiss Pass--so for two people a 2nd class pass would be $806:
http://ricksteves.raileurope.com/rail-tickets-passes/swiss-pass/index.html

It has better coverage of other parts of Switzerland like the Italian speaking regions of Lugano and Tirano. Infact, the BBC just just an great travel article about the line to Tirano:
http://www.bbc.com/travel/feature/20140612-the-swiss-train-tourists-dont-take

If you're like me and decide you want to spend more of your time going up to the panoramic vistas in the Alps and explore between Bern and Luzern, then the Berner Oberland pass is a little cheaper (but also requires additional tickets to get from Zurich & to lake Geneva from the Oberland).

I believe you can buy either Pass at the Zurich Airport train station.