From the south, we have Oxford American which embraces all things southern flavored and publishes articles on food and film and fashion in addition to the traditional fiction, poetry, and art. They also have some truly stunning covers. Virginia Quarterly Review is one of the classics, and stories published in it have gone on to won a number of big awards, including a National Magazine Award. Ecotone's mission is to create a discussion place, which makes it one of the few literary journals who consistently publish work about science and nature.
From the west coast we have Tin House - one of my personal favorites. They publish some seriously good writers while maintaining a free-spirit, unpretentious vibe. Zoetrope: All-Story, with a nod to its founder, Francis Ford Coppola, has a Classic Reprint section for stories that have inspired films. McSweeney's and The Believer, both published by Dave Eggers' publishing house, are hip, thought-provoking and fun.
Out of the UK we have Granta. Granta has been around for a very long time and has published an impressive list of internationally acclaimed writers, though they publish lesser known authors too. They were the first to publish Bill Bryson, Zadie Smith, and Arundhati Roy, among others.
This is just a small, small sampling. There are so many newer magazines experimenting with form and style and content. So come check out the shelves!