In my opinion, a literary journal that does not accept simultaneous submissions is the bane of a writer's existence (to use a cliché) because this means a journal is arrogant enough to say you can only send your work to them, and then wait around for weeks, often months, to hear back, and during that time you can't send it to any other journal for consideration. Your text is thus tied up for the duration, and given that the chance of being accepted typically lies between 1-5% for any journal, the process of having your work published virtually grinds to a halt.
I've explained my approach to submissions and to ranking literary magazines in previous posts and even though I clearly don't appreciate not being able to send my work to more than one magazine at a time, unfortunately some of the best literary magazines in the U.S. still do not accept simultaneous submissions. So, as previously promised, if you are willing to wait it out, here is my list of literary magazines that do not accept simultaneous submissions but are still worthwhile because of their reputation. Please keep in mind that this ranking is based on my own criteria of how often a magazine has received either a Pushcart for nonfiction or been included in Best American Essays over the last three years.
Journals are listed in alphabetical order:
The Threepenny Review
North American Review