I've got a subscription to two and read a few others periodically. The two I subscribe to are
The Paris Review and
McSweeney's.
The Paris Review is pretty straight forward content and layout wise and has been this way for over 50 years. Each issue contains two interviews with either author's of fiction, poetry, non-fiction, or journalism. In addition to the interviews, there is new fiction, poetry, and photo essays, art work, etc etc.
The interviews are truly wonderful reads. Last the magazine began to put all of the interviews in the magazine's history online, by decade. However, there are one or two omissions here and there of the likes of Hemingway, Faulkner, and one or two others due to rights issues. But it's an incredible resource if you're interested in the craft and process of writing.
Here is a
link to the section, The DNA of Literature. For most of the interviews posted, you can download them as a pdf and read/print if you so desire.
McSweeney's is the other journal I subscribe to and sometimes issues can really be hit and miss. You may get an issue thats designed like a packet of mail complete with spoof junk mail and what not. The next issue may then be a hardbound book with a DVD. Content wise, it seems to be in flux compared to a journal like
The Paris Review, but the editors of
McSweeney's openly state that they're not producing a journal like
The Paris Review or
Granta.
The other journals I read from time to time if something interests me in a certain issue are:
Granta and
Conjunctions.