Can Not Spit It Out
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There is a piece of vital information that would clear up a character's problems, whether it is a misunderstanding of romance or combat. If the character just spit it out, it would save entire episodes....entire seasons of trouble and tears.

....so, naturally, they don't.

Whether it's due to embarrassment, ego, or just plain stupidity, they rush into whatever situation is going on. Sometimes this leads to a moral about the benefits of clear-headed conversation over fighting needlessly. However, most of the time it's just to provide padding to the series.

Cant Catch Up
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Due to the Sorting Algorithm Of Evil, many anime have a habit of powering up their characters, season after season. However, this doesn't happen uniformly; the main characters are most often powered up, followed by whichever secondary characters are most popular with the audience, and then, sometimes, the rest of them. This can result in a situation where a character who was introduced as the hero's equal can slip further and further back in the power rankings, to a point where they can't even help out against the Monster Of The Week.

Dramatic Wind
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Before any fight begins or important truth is revealed, or if the character is simply standing and looking noble, a wind will invariably blow, ruffling his hair, the grass at his feet, and/or his cape if he's wearing one.

Even if he's indoors.

Hand Behind Head
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When nervous or uncertain -- or when lying -- a character will sometimes rub the back of his neck with one hand, often with a patently false grin or laugh accompanying the gesture.

Impossibly Cool Clothes
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Animated and anime characters can often be found wearing clothing that just looks too good to be real. This can be proven by the occasional attempt made to reproduce these clothes by the costume teams for live-action adaptations or by enthusiastic fans. Sometimes this is because of structural elements that flout or ignore real-world physical laws, or because the outfit in question requires an inhumanly perfect (or simply inhuman) body underneath it, or because real-world materials just don't look as good as ink and paint.

Clothing in animated series also shows near-indestructibility in terms of almost never ripping, fraying, staining or wrinkling, no matter what kind of stresses are placed on it or substances flung at it. Sometimes this is given an explaination (the material is some experimental or magically enhanced substance), but most times it isn't. And surprisingly, no one seems to question why Superman's suit never gets as much as a grass stain.

Any character with clothing showing signs of distress is truly in a world of pain, and possibly imminent death. Unless, of course, the character in question is a woman in Anime, as clothes-tearing near-misses are a hallmark of fanservice.

Note that despite the name given this trope, such outfits need not be cool, or even particularly good-looking.

Late For School
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Typical for shojo anime heroines. This is usually how their shows begin in the first episode.

Basically, they're never on time for school. While some are Heavy Sleepers, it would appear that they may have simply set their alarm clocks so as to give them insufficient time to get to class.

They will thus be in a frantic rush, which usually results in them taking short cuts, eating breakfast on the run, and bumping into important people in a manner that gets the plot of the series started.

Not So Fast
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A fair bit of Anime is adapted from Manga, its print cousin. There are good things and bad about this.

The trouble is that the narrative style of Manga derives from literature, where the amount of space you spend on something is proportional to how important it is, while the narrative style of Anime, like all of television, derives (even after all the tricks of Time Compression? and such are considered) from how long things actually take.

So you start out with, say, a 30 page comic book, and you want to turn it into a 30 minute show. This can be a problem if there's a fight scene: a comic book might devote an entire issue to a single fight, which only takes up about five minutes on-screen. And translating a monthly publication to a weekly series makes matters even worse.

As a result, characters in Anime derived from Manga tend to talk a lot.

A whole lot.

At totally inapropriate times.

Often, you'll have heroes spend entire episodes taunting each other mid-battle, explaining their last move in excruciating detail, Calling Your Attacks, building up their Battle Aura, gathering their composure for the next attack, adopting a silly pose, or reflecting on all the things they stand to lose if they don't win this one.

Parental Abandonment
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A stunningly large number of anime heroes and their coteries are lacking one or both parents, either through death or misadventure. Even if both parents are alive, they may well be emotionally or even physically distant.

This is a very convenient way for characters to be able to run off in the middle of the night to fight Evil, get sucked into another world, etc. without having anyone responsible for them making a fuss.

Pre Explosion Glow
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Everything emits light before it blows up, often in brilliant beams that work their way out of cracks in the surface of the doomed object. Often the object bulges like a balloon being squeezed before finally blowing to pieces.

Five Man Band
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The Five Man Band is a group of characters whose members fall into standard heroic archetypes which all complement one another.

The group traditionally includes:

The Hero - (lead singer) - the leader of the group; can be clean-cut and upstanding, bold and charismatic, serious and driven, or some combination of the three.
The Lancer - (lead guitarist) - the second-in-command, usually a contrast to The Hero. If the Hero is clean-cut, the Lancer is a grizzled anti-hero; if the Hero is the driven and straight-laced type, the Lancer is more relaxed and level-headed.
The Big Guy - (bassist or drummer) - the strongman of the team, often dumb. Or mute.
The Smart Guy - (keyboardist) - the weak, but intelligent or clever member, often annoying or for comic relief, a Trickster Archetype, a buddy of the Big Guy.
The Chick - (tambourine, vocal effects) - the token female who has been incorporated into the core group. Often of royal descent: Princess Allura (Voltron), Princess Leia Organa (Star Wars). The Chick will sometimes have special powers, presumably, to "even the field" a little. In all-female groups, The Chick will be the most "ditzy" member of the group.