"Do they enter random text or put in URLs where they shouldn't?"
A (somewhat) common thing to do is have a form field hidden with CSS. Spam bots rarely, if ever, parse CSS
Or, you have a form field labeled "Leave this field blank." Spam bots will usually fill in all available fields so, again, if it's got a value you just ignore it.
I'd mod you up, but I feel compelled to reply
I just signed up for Time Warner 'net myself, and when the dude was checking the signal he mentioned something about how there's a 25Mbit "boost" that people get at random. I didn't get a chance to ask many questions about it, but he said that it wasn't just an ISP-level cache