With online chess, the rules are usually given on the site. For non real time chess, such as correspondence chess (e.g. http://www.redhotpawn.com) consulting opening books or chess opening websites is allowed, but feeding your moves or position to a chess program is not allowed, though they can't stop you, and it's difficult to prove it.
The site I mentioned has forums where this subject has been discussed in great depth.
--
Oh Lord, won’t you burn me a Knoppix CD ?
My friends all rate Windows, I must disagree.
Your powers of persuasion will set them all free,
So oh Lord, won’t you burn me a Knoppix CD ?
(Missquoting Janis Joplin)