A bit hubristic to think this is all of them (and there are some hybrid forms), but here goes with a first attempt at a taxonomy:*
UPDATE, 29 MAY 2018: An 18th category of headline has been added: The voice of the protagonist (editorialised).
1) The simple declarative sentence

The first option to consider for straight news stories. Works at its best when the story is so good as to not require embellishment: NIXON QUITS, MEN WALK ON MOON, WHALE SWIMS PAST COMMONS. Can be used quite effectively to express opinion as well as facts (eg for leading articles). Doesn’t work for features, where it is important to signal the elevated quality of the writing in the headline, or interviews, where it’s much more interesting to hear the interviewee’s words verbatim. Exists in reversed form at the New York Times, with the prepositional phrase positioned at the start (“In Lower Saxony, An Artisan In Cheese Evokes Fond Memories”).
2) The existential emotion

Actually also a declarative sentence, but one that omits an understood existential clause (“There is”, “There are”, “There will be”) at the beginning in order to start with the exciting bit: anger, shock, horror, etc. Distinctively British.
3) The killer quote

Just the quote on its own, with no attribution or explanation. Effective when an opportunity to use it presents itself, which it rarely does, because without any annotation the quote will have to be both eye-catching and completely self-explanatory (at least for the web), which few ever are. (Even this one, from the BBC, inserts the word ‘also’).
4) The annotated killer quote

Ideal for interviews, vox pops and eyewitness stories: just find the most pithy phrase the subject says, and fill in the background afterwards. However, like the popular shopping-list and zingy-kicker headlines (see below), it usually requires a colon, which can mean the paper filling up quickly with kicker-style heds.
5) The voice of the author

A less demanding, paraphrased form of the killer quote, where the headline is written in the interviewee’s (or sometimes columnist’s) voice without actually being verbatim. Frequently begins with “My …”.
6) The then-and-now

The best way to approach large measures: however big your headline box is, this technique will fill it. Also works well for standfirsts. All the material you need is there in the body text, which is hundreds of words long: all you have to do is insert as much of the backstory as you need to take up the space, then follow it up with the news item in the first paragraph of the copy. Not useful for one-column NIB headlines.
7) The brusque rebuttal (aka the ‘No, the Earth isn’t flat’)

By far the most effective rebuttal headline, and the exception that proves the rule, observed in some newsrooms, that headlines should never begin with the words “No” or “Don’t”. Works because it begins with the denial, whereas any other contentious form has to begin with the subject of the dispute (“The Numbers On Toaster Dials Don’t … “) or a more abstract construction “(Why It Is Not True That ….”), which dissipates the impact. A relatively new form: perhaps that’s because it’s particularly effective when rebroadcast on Twitter, where directness is the standard mode of address.
8) The head-scratching question

A world full of questions also tends to generate journalism full of questions. Not exactly a recommended style, but often the only kind of headline you can write on pieces that fail to come to any solid conclusion. Usage per edition should be carefully rationed.
9) The insinuating question

Is this the most insidious headline form in Britain? As unscrupulous back benches know, a question headline means rarely having to say you’re sorry in the libel courts. Entirely different from the head-scratching question, because it knows precisely what it wants you to think. Ethically dubious.
10) The question-and-answer

The most respectable form of question headline, it at least has the courage to come a conclusion on its own. Good for comment and analysis pieces, as it gives the impression of a position being taken only after due consideration of the issues. Too indecisive-sounding for editorials, where the tone of certainty must be absolute.
11) The single-word shocker

GOTCHA! HORROR! WINNERS! OUTRAGE! Usually only for special occasions, or occasions you wish to imply are special.
12) The unparseable pun

An exclusively tabloid creation, often comprised of a well-known phrase, apposite to the story, with one word changed to reflect another aspect of the story. You can see the relevance of the first part; you can see the joke in the second part. But you can’t actually extract any sense out of the resulting sentence when you put the two together. A separate category from the standard tabloid pun headline, which is often a readily comprehensible sentence with homophone substitutions.
13) The zingy kicker

A joke, sometimes even an unparseable pun, but with an explanation afterwards to help you understand it. Another tempting headline form that requires a colon.
14) The flying verb

Omits the subject of the sentence (creating an “implied subject”) and starts with a verb. Almost exclusively American. Often baffling. Now very rare.
15) The columnist’s imperative

Voice of cold command, using the imperative mood, from the most authoritative figures in the land, viz one’s own opinion writers. Achieves its apotheosis in the form of the “open letter” (“DEAR PRINCE HARRY, don’t assume …”).
16) The how/why

Seductive and explanatory (and perilously easy to overuse). Gives the impression of an organisation with a high level of expertise and a mission to enlighten. Often a marker of the more highbrow publication. (The tabloid headline: I SLEPT WITH 1,000 WOMEN. The broadsheet headline: WHY I SLEPT WITH 1,000 WOMEN.)
17) The shopping list

Useful for nervous sub-editors confronted by legally complex stories with many moving parts. Also good if neither you or (you fear) the reporter fully understands the relationships between all the players in the drama, because it entirely dispenses with verbs; as we have previously discussed, verbs can get you sued.
18) The voice of the protagonist (editorialised)

Compact and effective quote-style headline in which the subject of the story’s words are pithily summarised, sometimes to his or her disadvantage. Far more editorialised than other quotation heds. Have caused controversy.
*I’ve attempted to classify headlines by rhetorical form rather than tone: most of these headline types can equally be funny or serious, punning or straight, while retaining the same essential structure
Tags: headlines, rhetoric