It's allowed in correspondence chess here but not in live chess. In fact, there is a Game Explorer database on this site that's made available for this purpose among others.
database cheating?
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The answer is that none of those things are against the rules for correspondence chess here, but are for live chess.
Against the rules for correspondence chess are endgame tablebases, the use of engines, playing back moves from other games and having multiple accounts. These activities will be detected and will get you banned.
Finally, discussions of cheating really should be directed here:
http://www.chess.com/groups/home/cheating-forum
Also, see Erik's first post here:
http://www.chess.com/forum/view/community/chesscom-policy-on-cheating
is it cheating to consult a large database while playing correspondence chess?
i just recently got a pretty big database with around 780,000 games which i haven't used yet, but i just wanted to make sure that i'm not doing anything wrong by looking at it during a game.