A brief explanation of grain lines is in this:
http://sewing.about.com/od/beginner1/p/fabricgrain.htm
I've found it helpful to wash fabrics before cutting for many reasons -
but one of the more useful ones is that the fabric will end up "doing what it wants to" after it has been washed. Sometimes it seems to "straighten out" - and then one can see how off-grain it had been on the bolt - sometimes it has been processed so it wants to stay off-grain.
(Think of what happens to "the girls" when the bra is removed :? )
I've learned that the ones that are still off-grain after washing want to be that way. Then I usually use them "as is" - and then decide if I want to make that first cut along the lengthwise or crosswise grain.
I've also learned to check for grain line on fabric before purchasing it. Every once in a while I forget - and regret it!