Having an art school background means that I've had to sit through any number (dozens, probably) of Art History classes... Some of the big 'principles' that come out of art history include:

• A strong sense of that which has come before. So many photographers approach photography in a vacuum... Having no idea (and often not caring) that art is built on the shoulders of who came before. Knowing something about Art History makes it possible to speak to whether a work is derivative (a capital insult in the art world), or homage (often a complement to both the person giving and getting the homage).
• Beginning photographers (especially ones who've only been photographers in the 'digital era') often rely on luck, volume (quantity of shots taken), and post-production corrections in order to get good photographs. An Art History education really trains the mind to be deliberate in all aspects of photography (lighting, subject, background, DoF, etc.) This is because spending a lot of time looking at the different ways others handle those same problems heightens awareness of them in the work you're doing, and having a library of techniques to draw on to emulate will often strengthen the work.
• Reoccurring patterns and motifs are illuminated. To watch how (for example) art's portrayal of the devil over the course of 500 years has evolved can inform my own work. Maybe a less extreme example... It is possible to see something like 'short lighting' being invented by observing painters draw inspiration from one another over the course of centuries.
• All of the above which leads to the 'big' principles of art history... A strong history of R&D in the art world- Rip off and Duplicate. Art evolves as the result of artists building liberally on other artists work over time, and there's no reason that Photography shouldn't draw from that well too.

In terms of resources:

• Crash on the floor in the Art section at a local 'big box' book store and leaf through all the big glossy books (and maybe you thought computer related books were expensive... I only manage to find $100+ books in the art section! I never buy, just look).
• The library can also great for looking at art. They also are less likely to frown at you if you spend hours looking but don't buy anything. :-)
• Paradoxically I often find the internet to be a hindrance to actually studying pieces of art... But that just may be me. I tend to find that most of time the pictures on the internet are too small to really get much out of... On the other hand, its never been easier to read the written histories of great (and more obscure) artists, which can really add depth to the works as you view them.
• Finally, there's absolutely nothing like actually viewing paintings (or photographs, for that matter) 'in person.' Visit a museum. Visit a gallery. Visit lots of 'em. If you're lucky enough to live somewhere that gets traveling exhibits that come to town, go see them, or go on vacation somewhere that has a reputation for great art.