UPDATED 11/20/2017
Below is a list of 88 no fee, literary magazines/journals that have a fast turnaround time (most average a month or less) according to Duotrope. 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.
 

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

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

Reservoir

DEADLINE: Reading periods vary, check site for details
SUBMISSION FEE: None
FORMS:  poetry, fiction, creative non-fiction and art
PAYMENT: None

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

Tuck Magazine

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'

Acumen
After the Pause
Allegro Poetry Magazine
Amaryllis [Poetry Swindon]
American Journal of Poetry, The $
American Poetry Journal, The
Anomaly Literary Journal
Anti-Heroin Chic
Apple Valley Review, The
(b)OINK
Bop Dead City
Buck Off Magazine
Calamus Journal
Cease, Cows
Chiron Review
Christian Century, The
Clementine Unbound
DIALOGIST
Dime Show Review
diode poetry journal
Dunes Review
Easy Street [The Lascaux Review]
Ekphrastic Review, The
Eunoia Review
FLAPPERHOUSE
Front Porch Review
Gamut
Gone Lawn
Great American Poetry Show, The
Gyroscope Review
Haiku Presence
Hamilton Stone Review, The
Hermeneutic Chaos Journal
Inflectionist Review, The
Into The Void
Jersey Devil Press
Leaves of Ink
Liminal Stories
Literary Yard, The
Mithila Review
MockingHeart Review
Modern Haiku
MOON magazine, The
Muddy River Poetry Review
New Verse News, The
Noble / Gas Qtrly
Not One of Us
One Sentence Poems [Ambidextrous Bloodhound Productions]
Plum Tree Tavern
Poetry Breakfast
Radar Poetry
Random Sample
Rat’s Ass Review
Red Eft Review
Red Paint Hill Poetry Journal [Red Paint Hill Publishing]
Riddled With Arrows MATURE
Rust + Moth
San Pedro River Review [Blue Horse Press]
Scarlet Leaf Review
Scifaikuest [Alban Lake Publishing]
Snakeskin
SOFTBLOW
Songs of Eretz Poetry Award Contest [Songs of Eretz Poetry Review]
Songs of Eretz Poetry Review
Star 82 Review (*82)
Third Point Press
Third Wednesday
Threepenny Review, The
THRUSH Poetry Journal
Tincture Journal
Typehouse Literary Magazine [The People’s Ink]
UCity Review, The
Valparaiso Poetry Review
Viewfinder Literary Magazine
What Rough Beast [Indolent Books]
Wildflower Muse
Writers Resist MATURE

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