Henry said:
The kinds of stylistic elements that immediately send me thinking "anime" are things like:
Enlarging one facial feature MUCH proportionally larger than the rest of the facial features to express emotion (huge smiles but small eyes in one shot, or huge eyes, but slit-like mouths in another shot on the same character)
Yeah, this is very much a stylistic quality of anime. Shows up in comedy anime more than in serious anime, but it is there. This is most likely a result of how every anime draws its roots from the work of Osamu Tezuka (which very much has these aspects), which in turn is directly inspired by Disney animation.
Character shots that either linger over one facial expression for many seconds, or repeatedly revisit that expression in cut scenes back and forth
Can't say that I know what you are talking about... Maybe you are refering to anime that is cheaply made? Reusing animation and overly long static images are hallmarks of a low-budget production.
Action shots that are repeated several times to enhance the effect
Yeah, this happens. It annoys me, too, but it is a trope seen in some anime. I wouldn't call it one of the stylistic elements that define anime, though...
character names that refer to actions, or common words ("Guts" in berserk, Cloud Strife in FF7, Alucard in Hellsing)
Keep in mind, these are names where the creators use the English words even in the Japanese version, so it is intended to have a slightly different effect for Japanese audiences. It is also important to remember that actual Japanese names are not terribly different. For example, a common Japanese name is "Yuuki", which literaly means "courage".
hair represented by "spikes" in differing patterns, usually to represent the "tousled hair" look
True, especially in works originating from a manga. This is an artifact of drawing styles, as well as a general way of creating interesting visual effect in an easy to draw manner (since animation needs as many shortcuts as possible in order to remain under budget). Not universal, though.
strong references to specific martial arts styles or "secrets" that one character knows but others don't.
This is only an aspect of particular genres of anime (martial arts/shonen anime, mostly), and is not at all different from how things in equivalent genres of other styles (Hong Kong martial arts films) work. Arguably, this is actually based in how martial arts historically functioned.
characters, even the protagonists, whose motives are inscrutable to the viewer (namely me), but often have to do with an unspoken code of honor or rules that they are loath to break, and when they do they seem far more upset about it than the situation would seem to warrant. Even Star Wars kind of borrows this meme when describing why anger is so inimical to the Jedi... it's only through further movies and writings where this is better explained.
I don't think I have seen anything that fits this description, really... Any specific examples to help me out?
Caveat: not all japanese anime has each of these elements, and some shows that are mroe "western animation" has some of these elements. However, these are all elements that most anime I have seen share. There are some, doing a little poking around, that don't seem to have these elements (Sorcerer Hunter, Witch Hunter Robin, Monster), but these seem to be the least referred to anime, more often hearing of Lodoss War, InuYasha, Naruto, Escaflowne, etc. which seem to share many of these traits, and unfortunately most of these traits, especially together, turn me off to that style. I'm not looking to be convinced, but trying to clarify the whole, "you don't like anime? You don't know what you're talking about" thing.
Ah, I see what is going on...
Keep in mind, only a small fraction of anime is talked about very heavily. There are two distinct subsets which get talked about the most: the mainstream and currently popular anime (which tends to fall into a very narrow realm of genre), and the older anime from before it became relatively mainstream, which has somehow establsihed a wierd anime "canon" taken from the 80's to early 90's.
The former category comprises Dragonball, Bleach, Naruto, One Piece, Inuyasha, etc. Of what I just said, all but Inuyasha were all published in the same magazine in their original manga form, a genre publication called Shonen Jump. You practically have to follow a certain formula of characters, plot, and ideology to get published in Shonen Jump. Inuyasha was published in Shonen Sunday, a magazine targetting the same audience and general genre as Shonen Jump.
The latter category, the anime "canon", is mostly stuff that is fairly popular and is consdiered iconic, but I hate a lot of it... Ninja Scroll is in this list, but I can't stand that movie.
As a whole, a lot of the anime that would appeal to a broader variety of tastes is the stuff that is
not talked about a lot.