There is an AMO minimum arrow weight chart. The common rule you will see is not to go less than 5 grns per pound of draw weight. However this is an IBO thing and is meant for bows set at a 30 inch draw length. It really depends on how efficient your bow is, what your draw weight is and what your draw length is. If you shoot a shorter draw length with a low energy cam or wheels you can get away with a lighter arrow than a guy shooting a longer draw length and high energy cams. It's all about how much energy your set up can put into the arrow. Not all set ups are equal. Don't tell me my girlfriends Rintec target bow set at 30 lbs with a 24 inch draw weight puts out as much energy as a bowtech black night set at 70 lbs and 30 inches of draw length. There is HUGE difference in efficiency between those two bows.

Most newer bows will handle a pretty light arrow without damage, especially if you have limb savers or some other vibration soaking device installed. keep in mind the more you shoot your bow with really light arrows the quicker you can wear it out. Vibration and shock are a bows worst enemy. It's not too good on your string either, which why my target bows even have string dampeners on them.

As far as hunting weights it really depends on what you are hunting and what your set up is. Most average sized people shooting a newer bow with a 300 plus IBO speed with 65-70 lbs of draw weight have more than enough energy in their set up to get pass throughs on deer, regardless of arrow weight. Now if you shoot a set up with less energy, like if you have a short draw length or something, or are shooting at larger animals you might want a heavier arrow that will carry more momentum. This will help your penetration. You give up trajectory for it though.
[font="verdana,arial, helvetica"] AMO Recommended Arrow Weight Chart

Paul