Many of the popular outdoor magazines have some type of solunar tables. These tables work on the premise that feeding activity will be heaviest when the moon is directly overhead, directly underfoot, or even with the skyline. With this reasoning, the best fishing should be around midnight on the full moon, noon on the new moon, sundown on the first quarter (half moon waxing), and sunup on the third quarter (half moon waning).
My personal experience is that sometimes the solunar times are on the money and sometimes they are dead wrong. Unfortunately, it seems like they have more accuracy if I don't pay any attention to them until after I fish. That doesn't help much if the whole purpose is to know when to fish and when to sleep, eat, look for new spots, etc. But it seems like everytime I think I am onto something, I get thrown for a loop and go back to the drawing board.
I believe that morning and evening are usually active periods. On the 1/2 moon, the morning and evening have the most lunar influence during those active periods. It seems to me that morning and evening truly are better during the 1/2 moon than new and full moons. So, in a sense, I believe in the solunar tables. On the other hand, I believe there is often a better feeding time when the moon first gets over the horizon. I believe the light of the moon is often a greater influence than the gravitational pull of the moon overhead. So, often the fishing is better the first couple of hours of moon up than it is when the moon is directly overhead (as the solunar tables say).