Whew .. loaded question there, as I've used various set-ups over the years.
Roughly 15 years ago, my go-to stereo still rig was two higher end Sony digital still cameras and a synchronization device to get the shutters to fire in sync. All loaded in a customized rig. Later built 3-D video rigs that I also used on occasion to take stills.
I've also shot stills with a 3D Bloggie (less than 1" I/A --- great for close-ups, poor for medium and wide shots) and also have a JVC 3-D videocamera (roughly 1 1/2" I/A) that also can shoot 3-D stills along with 3-D video.
A few weeks ago I happened to be at the Grand Canyon and found myself with just my smart phone. Along with snapping some panoramas, I also used the "cha-cha" method to snap a pic, move a few inches, and then take another image. Combine and then align the two images and "voila!", a true stereoscopic image. This method doesn't allow for moving subject matter, but luckily the Canyon wasn't going anywhere soon. ;-) When time permits, I could upload a sample if you're interested.