Now to respond to Chris, I suppose what I had in mind in the OP was the traditional concept of a form or set, like a classical Japanese kata. Although, if you've ever seen Wing Chun's "Siu Nim Tau", it isn't at all like the what most other systems would call a form at all ...it's totally stationary and doesn't involve any choreographed defenses against visualized attacks. Instead, it involves assuming a particular stance and structure, and performing a sequence of techniques almost like a recitation. Yet it is much more. Whether or not others call it a "form" is irrelevant to those who train it.
Ah, but here's the thing, Geezer, what you're describing as "classical Japanese kata" probably isn't, which is what I'm asking... The long string of solo movements associated with the term "kata" (from Karate) are realistically a Chinese training form, when it comes down to it (being taken from Chinese systems, imported to Okinawa, then to Japan). Japanese kata tend towards paired sequences, with only a few forms (most commonly in Iai) being solo (although they are still sometimes done as paired forms as well, as Tachiai versions with bokuto/wooden swords, or in a few traditions where the Iai is actually designed to be paired, such as Shinmuso Hayashizaki Ryu or Asayama Ichiden Ryu).
With that in mind, the dominant teaching/transmission method for traditional Japanese martial arts is kata, and that makes up the bulk of the training. With myself training in traditional arts more than anything else, then, as you'd expect, there's a lot of kata in what I do. To put a figure on it, I'd say there's about 750 unarmed kata and 360 weaponry ones in everything I do.
Something I should probably mention, in regards to the discussion of "knowing/understanding" the kata, as it pertains to applications, is that the kata, in our methods, is the application. There is no kata without it, and it's pretty much what it is is what it is... there isn't anything overly "hidden" in the actions. You hit them here, it's a hit. You grab here, it's a grab. You throw someone, it's a throw. A big part of that, obviously, is the fact that most of them are done with a partner, but even with the solo form (again, typically Iai), the application is fairly simply what it is.
In terms of complexity, they range from a very few movements (some of the "simplest" are a single responce to a single attack, such as some of our sword kata which are little more [physically] than a counter thrust) through to much longer sequences of "give and take", such as some of the longer unarmed kata in one of the systems, which has an attacking sequence of two punches, two kicks, then another punch, followed by an attempted throw, and an escape from the counter to the throw, while the defending side has a blocking and evasive sequence, a counter to the throw, then move in for the finishing strikes and throw to end.