Main Storyline (Fuyuki Holy Grail Wars)
Seven mages summon each one a legendary hero to battle for the wish-granting Holy Grail.
Narrative Order:
Fate/stay night (2006) aka "Fate Route"
Fate/stay night: Unlimited Blade Works (2014)
Fate/stay night: Heaven's Feel I. presage flower
Fate/stay night: Heaven's Feel II. lost butterfly
Fate/stay night: Heaven's Feel III. spring song
Fate/Zero
Fate/hollow ataraxia (Visual Novel only)
Chronological Order:
Fate/Zero
Fate/stay night (2006) aka "Fate Route"
Fate/stay night: Unlimited Blade Works (2014)
Fate/stay night: Heaven's Feel I. presage flower
Fate/stay night: Heaven's Feel II. lost butterfly
Fate/stay night: Heaven's Feel III. spring song
Fate/hollow ataraxia (Visual Novel only)
Obs: Fate/stay night (2006) is generally regarded as bad adaptation, so it's usually recommended to skip it, although it misses the biggest part of Saber's character arc.
Obs2: Heaven's Feel III has yet to be released (next year), but you can always play the visual novel or watch a playthrough on Youtube.
EXTRA Storyline (Moon Cell Holy Grail Wars)
128 Mages battle in a tournament format for the wish-granting Holy Grail inside a massive supercomputer on the moon which observes and records human history. (Why? You found out along the way)
Fate/Extra (game)
Fate/Extra CCC (game untranslated)
Fate/Extra CCC Fox Tail (manga)
Fate/Extra: Last Encore (anime)
Fate/Extella (game)
Fate/Extella Link (game)
Grand Order Storyline (Incineration of Humanity)
Chaldea, an organization in charge of observing and securing the future of mankind, find out that history has been disrupted and humanity is doomed, so they need to fix it.
Fate/Grand Order: First Order
Fate/Grand Order Chapters 1 to 5 (mobile game)
Fate/Grand Order - Divine Realm of the Round Table: Camelot (movies / date TBA)
Fate/Grand Order - Absolute Demonic Front: Babylonia (2019 anime season)
Fate/Grand Order Final Chapter (mobile game)
Fate/Grand Order Epic of Remnant (mobile game)
Fate/Grand Order Cosmos in the Lostbelt (mobile game)
Kaleid liner Storyline (Fate but magical girls)
Fate/kaleid liner Prisma Illya
Fate/kaleid liner Prisma Illya 2wei
Fate/kaleid liner Prisma Illya 2wei Herz
Fate/kaleid liner Prisma Illya 3rei
Fate/kaleid liner Prisma Illya 3rei: Oath Under Snow
Other spinoffs
Fate/Apocrypha - (watch it after the Main Storyline)
Carnival Phantasm - (watch it after the whole "Fate/stay night", you might want to read Tsukihime VN)
Today's Menu for Emiya Family - (watch it after the whole "Fate/stay night")
Lord El-Melloi II Case Files - (watch it after Fate/Zero)
Fate/strange fake - (light novel, read after "Fate/stay night")
Garden of Avalon - (drama CD, after "Fate/stay night (2006)")
Fate/Requiem - (light novel, read after "Fate/stay night")
Other Nasuverse works
Tsukihime (Visual Novel)
Kara no Kyoukai (Movie Series and Light Novel)
Kagetsu Tohya
Mahou Tsukai no Yoru