I don't know... if I used a random number generator to try thousands of credit card numbers against Amazon's order page, say, that would sure be illegal.
Amazon- and almost everyone for that matter- has measures in place to prevent this.
Computer-knowledgeable people frequently make a mistake with regards to the law, in that we get hung up on the specific techniques because we imagine hacking as some sort of sophisticated act. We think of breaking encryption or delving into the depths of a restricted system, not just running a script against a Web site, but the law doesn't really care about the technique. A huge amount of computer crime is very low-sophistication stuff.
That's why people make metaphors to physical security/locks -- the law doesn't care if the lock was very good, or even if the door was locked, or if someone left a window open by accident. Same thing with "hacking".
But the physical security lock analogy assumes private property; a public, corporate web site is more like a public store leaving the employee's-only section wide open and unmanned.