Ploughshares has been publishing exceptional work since 1971. The work published is traditional. You won't find text/image hybrids or white-space experiments here, just great storytelling. Most pieces are paywalled.
"I Looked For You, I Called Your Name," a short story by Lauren van den Berg
The Kenyon Review has been housed at Kenyon college for almost 100 years. A bit more innovative than other journals of its stature, KR publishes work by established as well as emerging writers. Login is required, but anyone can read five free pieces per month.
"We Can Start This Story," a short story by Tega Oghenechovwen
On Granta's sleek (and themed) online issues, you'll find a range of writing from refined memoir pieces to gritty fiction. While the journal does publish poetry, it is not its main focus.
"Yr Dead," a short story by Sam Sax
A journal that really needs no introduction. The New Yorker publishes the best brand new work by world-renowned writers like Haruki Murakami, Joyce Carol Oates, and Tracy K. Smith. Often, audio is included with each publication---so you can hear a piece straight from the source.
"Vision," a poem by Tracy K. Smith
Ecotone magazine's tagline is "Reimagining Place" and that aptly explains their mission to publish work that exists at the intersections of ecology and identity. Ecotone publishes both emerging and established writers.
"The Last Good Day," an essay by Hea-Reem Lee
Image aims to publish new writing and visual art that focuses on issues of faith and spirituality. The style is primarily traditional.
"Haptics of Blue," a poem by Jai Hamid Bashir
Since 1981, BOMB magazine has published pieces that exist at the crossroads of art and critical thought. While the bulk of their publications are interviews of artists by artists, BOMB also publishes innovative poetry, fiction and creative nonfiction.
"Two Betties" two poems by Anne Carson
Since 2004, Guernica has published new writing that isn't afraid to merge art and politics. The magazine also regularly creates special columns like The Cutting Room, which publishes work that writers had to cut from their books, and Spotlights which promotes new work by writers living outside of the West.
"The Smoke of the Land Went Up" a short story by Andrew Cominelli
Besides touting a cool, retro aesthetic, Always Crashing is a magazine devoted to publishing genre-defying pieces. Although they are a small, independent operation, they treat their contributors with care and even nominate for prizes.
"5 Poems," five poems by Lucianna Chixaro Ramos
For nearly 25 years, Diagram has served readers a unique mix of schematics and text/image pieces along with poetry and prose. The minimalist design lets you focus on the writing which ranges from the asemic to fairly conventional poetry. Below each piece you will also find a short note from the writer detailing their creative process.
"Pig Ears" a poem by Justin Davis
When we encounter poetry, it is more often than not confined to a page. But what if it wasn't? That's the question A Container mag is asking. Instead of publishing poems, A Container curates a series of projects that turn poems into real life objects. You can purchase these poetry objects on the site or settle for a Look Book which contains hybrid text and visual pieces.
"In the Crossed World of Animals" a series of poetry objects by Terri Witek
CTRL + V is a gorgeously designed online literary journal that publishes text and image collages as well as audio pieces and collaborations between artists and writers. What we experience as readers is an beautiful, immersive experience where each issue takes over the site.
"Re:" a text/image piece by Kinsey Cantrell
Creative Nonfiction publishes memoir, essay, narrative history, and narrative journalism. Through the Creative Nonfiction Foundation, they support writers of true stories by offerring educational opportunities.
"Ongoingness" an essay by Amber Taliancich
Poetry is the oldest monthly magazine dedicated to publishing poems in the English language. Aside from the monthly mag, readers can browse the extensive digital archives which includes works from (nearly) every major poet of the 20th century.
"Redeem" a poem by Rosalie Moffett
It's all in the name! Brevity publishes exclusively flash nonfiction and short craft essays as well as book reviews from world-renowned writers.
"Maternity as a Country" a flash nonfiction piece by Ocean Wei
Named after acclaimed writer Raymond Carver, Carve zine technically publishes poetry and nonfiction in addition to short stories---but it's clear that the mission is to honor Raymond Carver's legacy and what his short stories meant to readers around the world.
"Worms" a short story by Meera Rohit Kumbhani