My first exposure to martial arts training was in an American hybrid style called Tai Zen which was billed as a cross between karate and jiu-jitsu. I was thirteen and was way into Bruce Lee flicks and the Kung Fu TV series. I had no concept of what style meant and really couldn't care less, but the Tai Zen place was down the block from my house so that's where I began. The 'karate' portion of the class was spent practicing kicks and strikes with plenty of free-style sparring, while the 'jiu-jitsu' techniques encompassed standup self-defense drills utilizing joint locks and some throws, but no ground stuff. We trained on mats, used no hand or foot guards or head gear for fighting and paid as we went. At that time it was $4/class - no contracts. We didn't learn anything that resembled kata, nor were there any Japanese terms used. In fact nothing in the way of Japanese etiquette existed such as bowing or kneeling in seiza. The school advocated progressive resistance training and even had a small gym in the back with lots of free weights, benches and machines. It wasn't a traditional martial arts school, but that hardly mattered.
Like new religions, martial arts styles come and go. An Isshinryu karate instructor from my area that I briefly trained with (a 6th dan) actually created his own style (with his own name in the style's title), devised forms named after local towns (e.g., "Smithtown no kun" or something similar, no kidding) and promoted himself to 10th degree black belt. Due to lack of interest he eventually called it a day and returned to Isshinryu. Another guy opened an "American" Isshinryu dojo which, among other things, featured his modified version of the style's trademark vertical punch and a set of basic exercises that differed from the founder's.
In his book Okinawan Karate, Mark Bishop catalogues twenty-one recognized karate styles, a bit superfluous considering Okinawa is an island barely larger than Brooklyn. To say nothing of the karate that has been developed on mainland Japan and elsewhere. Even Aikido, which became codified after the Second World War as a result of the teachings of one man, now has about thirty distinct sects. Curiously, the art of Judo - the most senior of the gendai budo (modern Japanese martial arts) - never really branched off into the myriad of substyles that exists in other arts. Judo, for the most part, remains a single style unto itself, indeed a rare distinction.
Some of the newer, American systems are downright wacky. A while back I saw a clip on something called Combat Ki, a style purported to develop imperviousness to vital area strikes.
Haven't seen any of these guys in the UFC yet. I won't hold my breath waiting.