120 film is very widely available still. It was originally just 70mm wide movie film, cut for length and packaged as a short roll with a paper light-proof backing added. (Note: 35mm film was originally derived from this, too... Simply by splitting the roll lengthwise... at first without sprocket holes, then later with them added. 17.5mm and 16mm films were done by splitting 35mm film one more time.... And 8mm movie film was achieved by splitting it yet again.)
A lot of the film variations came about due to Kodak marketing efforts. Kodak bought the license and eventually got the patent to type 101 film, the first roll film, and soon came to love creating their own film format cameras, to try to lock in and monopolize customers for film and processing after the camera sale. This often worked for a while, until other camera and film manufacturers caught up with the changes. Then Kodak would change the format yet again. For a more complete list of film formats (mostly Kodak creations), see
http://en.wikipedia.org/wiki/Film_formatI haven't used it, but understand 116 film can be accomplished with 120 film, either re-rolling the film and/or with some slight modification to the camera.
120 film can be rerolled for use as 620 and 616 film, both also Kodak odd-balls initially. They really only differ from 120 in the size of spindle used inside the roll. The film itself is no different. Ostensibly, the slightly smaller 616 and 620 spindles allowed Kodak to make smaller cameras... but it's so little real difference I think this was just an excuse to come up with yet another film format and enjoy it's exclusivity for a while.
220 film is nothing more than 120 film packaged without the paper backing to be thinner, which in turn allows for a longer roll and twice the number of exposures. Because it doesn't have the light-proof paper backing, it cannot be used in older cameras that have the little red window on the back to display the frame numbers printed on 120's paper backing. And, due to the reduced thickness, many cameras capable of using 220 have a special pressure plate arrangement to help insure the film is held flat.
127 film is another Kodak spec that they originally made for their Vest Pocket cameras... but was soon adopted by many other camera and film manufacturers. It's narrower than 120mm film, but remains available in limited types at a few suppliers (B&H in NY has it... and a lot of other vintage format films).
110 and 126 were both very large format roll films prior to WWII, mostly intended for use in roll film holders fitted to glass plate cameras... But these same designations also were 1960/70's era miniature (26mm wide) cartridge films... All of these are more Kodak creations, of course!
I don't think you'll be able to find the larger, early 110 or 126 roll films, if those are what you're seeking. However, cameras in those formats should also be able to used sheet film in holders... or may be possible to modify to use it... most likely in today's 4x5", 5x7" formats or similar.
If you are seeking the 110 and 126 cartridge films, search the internet. I'm sure you'll find a few suppliers and processors.
If you shoot black & white, with many of these films (aside from the cartridges) you could simply process the negatives yourself. You don't even need a dark room... a simple changing bag and light proof developing tanks will work (after you learn to load the film by touch alone). Some chemicals, a timer and thermometer, and you're all set. As to making positive prints from the negs, with some of the larger image size formats, direct contact prints might suffice (no enlarger needed). If you want to put a darkroom together and do enlargements too... that should be easy and relatively cheap if you shop the used market. "Fume room" gear sells for pennies on the dollar, compared to what it originally cost. I still have much of my darkroom in storage... I just can't bring myself to sell it for so damn little money! :( But, hey, maybe some day I'll have time and space to set it up and use it again... if not, I'll let my heirs deal with it (might be collectible, by then!)
If you want to shoot color, it's going to be a lot more of a challenge to find films and processing for anything other than the relatively standard 120 (or the formats similar enough in size to be respooled from 120).