There are a few methods to view 3D at home.
3D Blu-Ray and a 3D monitor or projector (usually designed as a 3D TV, though converter boxes exist to use 60 Mhz or faster 2D TVs). Two types of 3D glasses are used; some sets are “passive,” using circularly polarized glasses, and some sets (and current projectors and convertor boxes) are “active,” using LCD shutter glasses. Passive sets have a polarization film imbedded in/on the screen, and show both eyes’ frames simultaneously, interlaced. The polarization allows the glasses (which are identical to Real 3D glasses you get at the theater) to filter out the proper image for each eye. LG and Vizio are the two main brands available; with an upgrade to firmware, LG sets provide a 1080i image for each eye. Active glasses (Sony, most Samsung, projectors, as well as 3D converters) use powered glasses that are more expensive; the TV alternates between images for each eye, and the glasses flicker the lenses alternately in sync. Ideally, an active set will be 240 Mhz; this allows 120 Mhz for each eye. Slower sets will provide slower Mhz to each eye, and a viewer is pushing it by using a 60 Mhz set, only getting 30 Mhz to each eye, often with noticeable flicker.
Most 3D Blu-Rays are properly done to spec, with both images interlaced together; however, a small number use other methods (side-by-side, top-bottom) that squish both images together onto one video frame, and the TV must then convert each half of the screen into its own frame by stretching them out to fill the screen, with lower resolution. I’ve only run across one commercial release like this, though (an adult film from Germany), but it’s common to find SBS or T/B for 3D video clips. YouTube does 3D playback, too, and you can have the YouTube player convert the video on the fly to any of the main formats or anaglyphic.
Field-sequential “active” glasses and 2D monitor. Pretty much identical to the 3D converter boxes above, but with less support. Typically used with NTSC CRT sets. FS has been around for a while (existing for VHS, VHD, DVD, and pre-3D Blu-Ray) but poorly supported, with few legitimate releases over the years which are all out of print (mostly scenery discs, with some studio support on occasion, especially the Robert Rodriguez family films). Slow and flickery, the screen alternates back and forth and the shutter glasses stay in sync. A burgeoning hobbyist scene in years past meant that a lot of unauthorized releases did exist, and it was common for 3D VHD releases from Japan (Emmanuelle 4, Jaws 3D, etc.) to get pirated here. This was also the method used by most early 3D video games-- the Famicom, Sega Master System, and the Amiga all had games and LCD glasses available.
Anaglyphic glasses and 2D color monitor. The “red/blue” glasses people still think of for 3D; each eye’s image is tinted the appropriate color, then the glasses filter the images out. Most 3D releases on VHS and DVD are in this format, and before 3D Blu-Ray came out, most 3D releases in Blu-Ray were in this format (Beowulf, Hanna Montana concert). A few 3D releases on Blu-Ray are available in both anaglyphic and proper 3D: My Bloody Valentine, The Polar Express, and others.
As to whether a 3D Blu-Ray plays back in 2D, part of the 3D Blu-Ray spec requires 2D to be available on 3D releases. Some studios put both on the same disc (sometimes as separate encodes, sometimes with playback being of one eye’s image only), while others package a separate 2D and 3D disc together. I have yet to purchase a proper 3D Blu-Ray that doesn’t have a 2D playback mode.