Okay... here goes:
(I will be including his "Dunsanian" tales because, despite not often directly using the Mythos paraphernalia, they came to be extremely closely intertwined with the Mythos, either through Lovecraft's mention of things from the earlier tales in his later work, or through the adoption of them into the Mythos by others. Ditto with the Randolph Carter tales....)
"Dagon" (1917)
"Nemesis" (verse) (1 November 1917; included for adumbration of themes and ideas later explored in the Mythos)
"Astrophobos" (verse) (ca. 25 November; ditto)
"Polaris" (1918)
"A Cycle of Verse: Oceanus, Clouds, Mother Earth" (November-December 1918; it has been argued that many of the motifs, and some of the basic ideas, of the Mythos see expression here -- I'm tempted to agree)
"The White Ship" (Nov. 1919)
"The Nightmare Lake" (verse) (December 1919; I include it as, in some ways, almost a verse version of the following story....)
"The Doom That Came to Sarnath" (3 Dec. 1919)
"The Statement of Randolph Carter" (December 1919)
"The Terrible Old Man" (28 January 1920)
"The Cats of Ulthar" (15 June 1920)
"Celephaïs" (early Nov. 1920)
"Nyarlathotep" (early December 1920)
"The Nameless City" (January 1921)
"The Quest of Iranon" (28 February 1921)
"The Other Gods" (14 August 1921)
"Azathoth" (fragment) (June 1922; first mention of the name)
"The Hound" (September 1922)
"The Rats in the Walls" (August-September 1923)
"The Unnamable" (September 1923)
The Festival (1923)
"The Call of Cthulhu" (Summer 1926)
"Pickman's Model" (1926)
"The Strange High House in the Mist" (9 November 1926)
The Dream-Quest of Unknown Kadath (late 1926-22 January 1927)
"The Silver Key" (ca. Nov.? 1926)
The Case of Charles Dexter Ward (January-1 March 1927; included not only for the -- very vague -- mention of "Yog-Sothoth", the first such in his work, but for links to his themes and concepts in later work)
"The Colour Out of Space" (March 1927)
"The Very Old Folk" (2 November 1927; dream-account, from a letter; a very similar passage later incorporated into F. B. Long's The Horror from the Hills)
"The Last Test" (revised for Adolphe de Castro; 1927; included for various hints of the Mythos)
"History of the Necronomicon" (1927)
"The Space-Eaters", by Frank Belknap Long (ca. Autumn 1927)
"The Hounds of Tindalos", by Frank Belknap Long (pub. March 1928)
"The Curse of Yig" (revised -- read: ghost-written -- for Zealia Bishop; 1928)
"The Dunwich Horror" (Summer 1928)
"The Electric Executioner" (revised for Adolphe de Castro; ca. 1929; Mythos combined with Mesoamerican mythology, though largely tongue-in-cheek)
"The Tale of Satampra Zeiros", by Clark Ashton Smith (16 November 1929)
"The Outpost" (verse) (26 November 1929)
The Horror from the Hills, by Frank Belknap Long (1929)
Fungi from Yuggoth (verse; sonnet cycle) (27 December 1929-4 January 1930)
"The Mound" (revised -- see above -- for Zealia Bishop; December 1929-early 1930)
"Medusa's Coil" (ditto; May 1930)
"The Door to Saturn", by Clark Ashton Smith (26 July 1930)
"The Whisperer in Darkness" (24 February-26 September 1930)
"The Return of the Sorcerer", by Clark Ashton Smith (6 January 1931)
"The Testament of Athammaus", by Clark Ashton Smith (22 February 1931)
At the Mountains of Madness (February-22 March 1931)
"The Black Stone", by Robert E. Howard (pub. November 1931)
"The Nameless Offspring", by Clark Ashton Smith (12 November 1931)
"The Shadow Over Innsmouth" (November?-3 December 1931)
"The Dreams in the Witch House" (January-28 February 1932)
"The Thing on the Roof", by Robert E. Howard (pub. February 1932)
"The Tree-Men of M'Bwa", by Donald Wandrei (pub. February 1932)
"Ubbo-Sathla", by Clark Ashton Smith (15 February 1932)
"The People of the Dark", by Robert E. Howard (pub. June 1932)
"Lair of the Star-Spawn", by August Derleth and Mark Schorer (pub. August 1932 [written summer 1931?]; Lovecraft provided the title for this one, and this is where the Mythos as it is viewed today begins to take form, with the battle between the Elder Gods and the Old Ones)
"When Chaugnar Wakes", by Frank Belknap Long (verse) (pub. September 1932)
"The Man of Stone" (revised -- see note on Zealia Bishop above -- for Hazel Heald; 1932)
"The Horror in the Museum" (ditto; October 1932)
"Worms of the Earth", by Robert E. Howard (pub. November 1932)
"Through the Gates of the Silver Key" (with E. Hoffmann Price; October 1932-April 1933)
"The Thing That Walked on the Wind", by August Derleth (pub. January 1933)
"Winged Death" (revised -- see above -- for Hazel Heald; 1933)
"Out of the Aeons" (ditto; 1933)
"The Thing on the Doorstep" (21-24 August 1933)
"The Coming of the White Worm", by Clark Ashton Smith (15 September 1933)
"The House of the Worm", by Mearle Prout (pub. October 1931)
"The Book" (fragment) (ca. late 1933)
"The Lady in Gray", by Donald Wandrei (pub. December 1933; loosely related to the Mythos)
"The Shadow Out of Time" (November 1934-March 1935)
"The Secret of the Tomb", by Robert Bloch (pub. Mar. 1935)
"The Suicide in the Study", by Robert Bloch (pub. June 1935)
"The Challenge from Beyond" (with C. L. Moore, A. Merritt, Robert E. Howard, and Frank Belknap Long; August 1935)
"The Shambler from the Stars", by Robert Bloch (pub. September 1935; HPL wrote a response to this one, "The Haunter of the Dark", to which Bloch in turn replied some years later with "The Shadow from the Steeple")
"The Warder of Knowledge", by Richard F. Searight (c. September-October 1935; member of the Lovecraft circle, Lovecraft read and had input on this addition to the set)
"The Diary of Alonzo Typer" (revised for William Lumley; October 1935)
"The Haunter of the Dark" (November 1935)
After this point, HPL was no longer writing any fiction that "belongs" to the Mythos, though he had read (and had input on) several remaining stories by Robert Bloch (collected together in Mysteries of the Worm), Henry Kuttner (collected together in The Book of Iod), etc., etc., etc. It was after Lovecraft's death that the majority of Derleth's stories -- which are really what gave shape to what was to become known as the Mythos -- were published: "Spawn of the Maelstrom", with Mark Schorer (written around the same time as the previous entry); "The Horror from the Depths" (ditto); "The Sandwin Compact", "Beyond the Threshold", "Dwellers in Darkness", "The Trail of Cthulhu", etc.; not to mention those "posthumous collaborations" where he took fragments or notes from HPL and wrote the rest himself: The Lurker at the Threshold, "The Watcher from the Sky", "Something in Wood", "The Whipporwills in the Hills", etc., which only ended with his death and the unfinished "The Watchers Out of Time"....
I may have missed a few by other writers during HPL's lifetime -- it was a hurried list cobbled from several sets of notes from over the years -- but the bulk of it is there. (I did not leave out anything from HPL that I can think of, however.)
A further note on some by other writers: HPL's mention of certain things created by other writers, by pulling those items into what became the Mythos (with Lovecraft, it was more a case of weaving a net of allusions, or coloring, rather than creating a genuine series or "mythos" per se), ended up leaving things open enough that several series by others can be said to be at least connected to the Mythos: Howard's Kull, Conan, and Bran Mak Morn tales (especially the latter, and "The Shadow Kingdom" of Kull); Kuttner's "Elak of Atlantis" stories; Smith's "Hyperborea", "Poseidonis", "Averoigne", and "Zothique" cycles; etc., etc., etc.
