I tried it one year. One thing I found was that the bales shrank a ***lot*** over the course of the season, and the shrinkage was uneven. I think it would help to have some kind of containment for the bales, such as wood sides. The other thing I found is that they need a lot of watering. I wished I had laid out a soaker hose over the top of the bales, connected to the faucet with an automatic timer. As I recall, watering with a hose often resulted with a lot of the water dribbling down and away from the plants; slow, frequent watering would have been better for the plants and also conserved on water usage. Also, I'm no expert, but I think it would have helped to have spread out at least a one-inch or two-inch layer of soil over the hay bales. If you are going to garden in the same place year after year, I think this would combine with the broken-down hay to form a nice base for a raised bed.
Edit: I should add that there seems to be a lot more information on the web nowadays, and a lot of the things that are recommended in the following website are things I didn't do. I didn't condition the bales, for example, and I have no idea if I had the cut side up. Plus, as you can probably tell from my calling it hay, I'm not a farming type person. I believe there is a difference between hay bales and straw bales.
http://bonnieplants.com/library/how-...-a-straw-bale/
I still think laying a soaker hose on top of the bales and setting up an automatic timer for watering would be very helpful.
Edit 2: Oh, my! This website makes me want to try it again!
http://modernfarmer.com/2013/07/straw-bale-gardening/
Edit 3: I think it's a good idea to read the negative reviews about the book before starting. Gives you an idea of some of the pitfalls.
http://www.amazon.com/Straw-Bale-Gar...dp/1591869072/