UPDATED 11/16/2019
Below is a list of 80 no fee, literary magazines/journals that have a fast turnaround time (most average a month or less). I’ve also researched and added some others to the list, based on suggestions from experienced writers. The list is long, so I wasn't able to provide additional details or links for all of them. Those that I've featured on my blog previously are detailed below, followed by a list of all the rest.
Read the guidelines carefully. Some may have changed whether or not they charge submission fees since I compiled the list. Some may be temporarily closed to submissions.

POETiCA REViEW

DEADLINE: Always open
FORMAT: online
SUBMISSION FEE: None
PAYMENT: None
FORMS: poetry

Into the Void

DEADLINE: Reading periods vary, check site for details
FORMAT: Digitally and print issues available
SUBMISSION FEE: None, until monthly free allotment is reached
Until we reach our Submittable-allotted monthly free submissions limit, there is no fee to submit but free submissions fill up extremely quickly. Thereafter you may submit via the Tip Jar but free submissions will resume on March 1st. Tip Jar submissions are a vital source of the income that allows us to run day-to-day, and are hugely appreciated.
PAYMENT: $5/page via PayPal only
FORMS: fiction, poetry, nonfiction, visual art

isacoustic

The Bitter Oleander

DEADLINE: Always open
SUBMISSION FEE: None
FORMS:  short fiction, flash fiction, and poetry
PAYMENT: None
NOTES: You can read more about them on The Review Review's site, including a four star review by yours truly here: International Mag Features Diverse and Imaginative Writings and Translations, Review of Bitter Oleander, Spring 2015 by Trish Hopkinson

Califragile

DEADLINE: Always open
SUBMISSION FEE: None
PAYMENT: None
FORMS: poetry
NOTES: "We will try to respond within 3 weeks. But if you have not heard from us in 1 month, we have passed on your work."

Glass Poets Resist

Ilanot Review

LOCATION: Israel
READING PERIOD: Reading periods vary, check site for details
SUBMISSION FEE: None
NOTES: You can read more about them on The Review Review's site, including Josh Medsker's five star review of their Winter 2013 issue, as well as an interview with editor Janice Weizman by Stanley Trice.
FORMS: Poetry, Fiction, Creative Non-fiction, Graphic Art
PAYMENT: None

Lunch Ticket

DEADLINE: Rolling
SUBMISSION FEE: None
PAYMENT: None
FORMS:  poetry, fiction, creative nonfiction, flash prose (any genre), young adult (13+), literary translation & multi-lingual texts, and visual art (painting, drawing, photography, printmaking, sculpture, installation, performance, and video)

The Penn Review

DEADLINE: Reading periods vary, check site for details
SUBMISSION FEE: None
PAYMENT: None
FORMS: poetry, fiction, creative nonfiction, and visual artwork

Sonic Boom

DEADLINE: Reading periods vary, check site for details
SUBMISSION FEE: None
PAYMENT: None
FORMS: experimental poetry, Japanese short-forms, flash fiction, and visual art

Street Light Press

DEADLINE: Always open
SUBMISSION FEE: None
FORMS: poetry, prose poetry, visual art
PAYMENT: None

West Branch

DEADLINE: Reading periods vary, check site for details
SUBMISSION FEE: None
PAYMENT: $50 per submission of poetry, and $.05/word for prose with a maximum payment of $100
FORMS: poetry, fiction, creative nonfiction, and translation

Wildness

The Rest of the List'

Radar Poetry
Literary Yard
Academy of the Heart and Mind
Eunoia Review
Red Eft Review
Nine Muses Poetry
Plum Tree Tavern
Isacoustic
The Threepenny Review
The Journal of Compressed Creative Arts [Matter Press]
Amethyst Review
THRUSH Poetry Journal
The New Verse News
The Christian Century
Front Porch Review
SOFTBLOW
Sonic Boom
Apparition Literary Magazine
Acumen: A Literary Journal [Acumen Publications]
Burning House Press
The Penn Review
Eastern Iowa Review [Port Yonder Press]
Clementine Unbound
Third Wednesday
The Inflectionist Review
Impossible Archetype
Your Daily Poem
Writing In A Woman’s Voice
Scifaikuest [Alban Lake Publishing]
San Pedro River Review [Blue Horse Press]
After the Pause
Dodging The Rain
Rat’s Ass Review
Riggwelter
Neologism Poetry Journal
Dreams & Nightmares
Gone Lawn
Rust + Moth
Down in the Dirt [Scars Publications]
Not One of Us
Jersey Devil Press
Ancient Paths Online [Ancient Paths]
Anti-Heroin Chic
Allegro Poetry Magazine
diode poetry journal
misfitmagazine.net
Prune Juice: Journal of Senryu & Kyoka
The Shore
Mobius: The Journal of Social Change
Bending Genres
Uncanny Magazine
Amazing Stories
Kissing Dynamite [Kissing Dynamite Poetry Press]
The Orchards Poetry Journal
Up the Staircase Quarterly
Prole
Valparaiso Poetry Review
Claw & Blossom
Failed Haiku: A Journal of English Senryu
Tagvverk
Third Point Press
Songs of Eretz Poetry Review
Moonchild Magazine
Halfway Down the Stairs
Modern Haiku
Bridge Eight Literary Magazine [Bridge Eight Press]
West Branch
Constellations
Empty Mirror
One Sentence Poems [Ambidextrous Bloodhound Productions]
Amuse-Bouche: Spotlight [Lunch Ticket]
Atrium
Vita Brevis Poetry Magazine [Vita Brevis Press]
Frogpond
The Lake
The Apple Valley Review
Green Briar Review
On The Seawall
Into The Void

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