Let's get one thing straight: If you're doing The New York Times crossword puzzle in the bathroom at work, you can't write off your daily Times subscription on your taxes as a professional expense. But it is actually possible to write off magazine subscriptions or trade publications as an itemized deduction, if you're actually using them for business development. (And while a daily subscription to the Times is a bit broad to meet the criteria, it might be possible to claim it if you can argue it's necessary to keep up with developments in your profession.)
Mostly, you'll want to make sure the publications are quite specific to your line of work. There are some rather obvious ones: If you're a scientist, you can easily write off journals or publications that cover your field. But professional dog walkers could just as legitimately write off their monthly bills from Modern Dog. (Or maybe even Cat Fancy: Know your competition, and all that.) Just remember to keep receipts and bills, and don't try to get too cute when justifying "professional and trade publications" with the IRS: They know that reading Maxim every month isn't really making you a better graphic designer.