Instamatic...

So, cameras that used roll film (as opposed to sheet film, like that used in large format cameras) generally required the user to thread the end of the roll onto a takeup spool. In an attempt to make a more user-friendly volkscamera sort of experience, Kodak launched the 126 film format in the early Sixties.

Dubbed the "Instamatic", a name obviously intended to signify ease of use, the film was all spooled up in a little plastic cartridge which you could just drop into the camera and then remove when you'd shot up all the exposures. The film itself was about the same size as 35mm film, but the camera exposed square images on it.

About a decade later, Kodak followed up with a second Instamatic film format, the 110. This used film that was as wide as the 16mm film used in subminiature cameras, but with only one row of indexing holes. The frames were half the size of a 35mm negative (the same size as a current Micro Four Thirds camera sensor, coincidentally.)

To combat worries that the film would be too grainy if enlarged to a useful size, Kodak even came up with new emulsions that would permit decent sharpness with 5x7s, maybe even 8x10s with good glass.

Unfortunately the vast majority of 110 cameras were cheap, plastic-lensed abominations, and the reputation for taking poor pictures has stuck with the format. Most customers' 110 photos I printed at the lab were garbage.

What the 110 format allowed, though, was the first advent of the take-anywhere, truly pocketable camera. There were some decent ones on the market, too; built well, with quality glass.

Pentax made an entire interchangeable-lens SLR camera system in the 110. The lens that's on there is the standard prime, a 24mm f/2.8. (Since the negative is half the size of 35mm, that gives the same field of view as a 48mm lens on a regular full-frame camera.)

Interestingly, the shutter also functions as the aperture, so all lenses have the same maximum aperture of f/2.8. It's a real SLR, with a pentaprism, TTL light metering, the works. Pentax sold a suite of lenses, a flash, a motor-drive/grip, and other accessories. They made them from '78 until '85.
 

Rollei's A110 is a little metal brick of a camera that is slid closed and then open again to advance the film, like a Minox spy camera. The 23mm f/2.8 lens has a reputation for being one of the better 110 lenses made.

Fujifilm discontinued 110 film production in 2009, but you'll find some in cold storage on eBay and elsewhere, and Lomography started producing it in 2011. I just got a roll from Amazon that I'm going to use to test the little A110 and see if it works!
.