Here is a preliminary overview of the anthologies.

In 1945 Alfred Hitchcock was approached by Dell to put together and introduce an anthology of suspense stories which was published as Suspense Stories Collected by Alfred Hitchcock, and reprinted several times with different titles over the next few years. It was an odd mishmash of stories, but despite being a little all over the place it proved successful, and in about a decade Hitchcock would find himself marketed to the extreme. In 1946 Dell Books released the follow-up Alfred Hitchcock Presents: Bar the Doors, arguably the best of all the first series of anthologies borrowing his name. By the end of 1949 a total of six books were published, followed by a hiatus that lasted until 1957.
In 1955 CBS helped launch what was to become among the most successful and longest-running television anthology dramas, Alfred Hitchcock Presents. Hitchcock himself directed the first episode, "Revenge," and three more episodes for the opening season. December of 1956 saw the first issue of the still-running Alfred Hitchcock's Mystery Magazine, and soon the anthologies were revamped full force. In 1957 one of the more popular anthologies was published by Simon & Schuster: Alfred Hitchcock Presents: Stories They Wouldn't Let Me Do on TV, ghost edited by Robert Arthur. (It became so popular that not only was it extensively reprinted over the years, the network backed away and allowed him to "do" many of the included stories.) These three ventures became intertwined. The magazine published original suspense stories, the television show adapted many of them, and the anthologies eventually became reprint venues for the magazine stories.
Among the writers who benefited from this trio of projects was the prolific Robert Bloch, whose short stories were frequently published in the magazine, and eventually adapted, many by his own hand, for the television show (a total of ten episodes for the original series and seven more for the extended Alfred Hitchcock Hour). It was perhaps through this collaboration that Hitchcock later came across the 1959 novel Psycho, the rights of which he quickly purchased. (In fact he also went ahead and purchased as many copies of the book he could find just so that his potential audience would be less likely to know the ending to his film adaptation.)
Another writer to benefit was Henry Slesar, who wrote several teleplays for a variety of shows throughout the 1960s, including Batman and The Man from U.N.C.L.E. Slesar had a record thirty-six teleplays or adaptations for AHP, with ten more for AHH, as well as one for the 1985 AHP remake pilot and three for the actual show. His stories were so adaptable and many of them well adapted indeed, that two paperback collections of his adapted stories were published under Hitchcock's name: Alfred Hitchcock Handpicks and Introduces A Bouquet of Clean Crimes and Neat Murders (NY: Avon, 1960) and Alfred Hitchcock Introduces A Crime for Mothers and Others (NY: Avon, 1962).
The anthologies were published in the US and the UK, successful on both sides of the ocean, but the magazine fared well only in the US. The British version lasted eleven issues, from September 1957 to August 1958 (no issue appeared in July), and later for five issues between May and September 1967. The Australian version, titled Alfred Hitchcock's Suspense Magazine, was published in 1957 and 1958, though I haven't yet been able to figure how many issues were printed, since it appeared to have gone through a reincarnation or revamping of sorts after #11.
In the 1960s

Another ghost editor in the mid-sixties was British anthologist Peter Haining, who ghosted a handful of collections for Pan Books in the UK. The only other person I am aware to have ghosted one of these anthologies is Harold Q. Masur, who put together the 1973 Stories to Be Read with the Lights On. This may have been a result of the unfortunate passing of Robert Arthur in 1969.
Throughout the 1960s and 1970s the adult anthologies were being published regularly, and each ran through various reprints. An annual hardcover anthology appeared and was reprinted as two separate paperbacks, first with the original titles or variations of, as well as completely different titles. (For instance, Stories for Late at Night was published as 12 Stories for..., More Stories for..., and later on simply as Skeleton Crew.) Other collections were retitled after minor changes were made, such as Suspense Stories which, with the addition of another story, became 14 Suspense Stories to Play Russian Roulette By, and later 14 of My Favorites in Suspense; these are all the same book.
The early anthologies were excellent works, especially those ghosted by Robert Artur, who selected a truly wide array of short stories, novelettes and even novels of a variety of genres and styles. By the 1957 revamping of these books, Hitchcock himself had little to do with the publications (by little I mean nothing, as I suspect that even the brief introductions were ghost written; there is a distinct difference in approach and tone with those published in the 1940s, and let's remember, Arthur himself was well practiced in putting words in Hitchcock's mouth, since he made the director a character in his Three Investigators series). It is truly unfortunate that Arthur never gained the recognition as a first-rate editor, though I am certain he enjoyed his career, working not only on these books but on his own writing and on the scripts for the AHP television show.

By the 1970s the annual hardcover publications became reprints of more recent work, primarily from the most widely read mystery magazines of the time: Alfred Hitchcock's Mystery Magazine, Ellery Queen's Mystery Magazine, The Mike Shayne Mystery Magazine. Soon the anthologies would become straightforward reprint venues for the magazine. Davis Publications, through their Dial Press imprint, published annual and sometimes bi-annual (it peaked as a quarterly in 1983) numbered anthologies which were essentially "best of" the magazine selections from the previous year. These were initially edited by then magazine editor Eleanor Sullivan (claimant of the first non-ghosted Hitchcock anthology) and later Cathleen Jordan; the first was published in 1976. By then the magazine had been publishing monthly for twenty years and had accumulated enough material to print any number of anthologies reserved for only AHMM stories; some stories even re-appeared in many of these collections so that the books were truly less than unique.
The late 1970s brought about a new era in presenting these works, with the hardcover editions employing titles along the lines of Tales to Take Your Breath Away, Tales to Keep You Spellbound, Tales to Scare You Stiff and so on, while their softcover counterparts were simply numbered, beginning with Alfred Hitchcock's Anthology #1, though later had their own, less clever, subtitles, along the lines of Death-Reach, Fear and Borrowers of the Night. I'm not yet sure when the hardcover editions stopped printing, but the numbered anthology publications ceased in 1989 with Anthology #27: Murder & Other Mishaps. Furthermore, these works were no longer ghost edited though still introduced by "Alfred Hitchcock" (sometimes bearing his signature in print).
It is really

[Note: It is frustratingly difficult to find accurate information on these publications, so much of what I have put together here is educated speculation, which means it sounds valid but could be utterly incorrect. Anyone with information to share, please do so; comment or for anonymity email me at casual.debris@gmail.com.]