Back in November of 2006, I had been travelling pretty extensively to Asia and Australia. My passport covers lamination was getting really bad (it was basically separating about 1 inch into the corner of my photo page. Never really had any problems with it until I exited Australia where I was stopped by the immigration official and a supervisor had to be called over. From there they took me to a room, questioned me (nothing major to be honest) for about 20 minutes, then spent about 20 minutes lecturing me on how it would be noted that if I tried entering the country again using this passport I would be denied entry and how could I ever travel with a damaged passport, what was I thinking, etc. I didn't really worry too much about it because I figured worst case I'd get deported to home and could sort it all out, but it was still not the best experience. I ended up getting a new passport after that (mine was expiring in about 7 months at that point anyway), so I didn't get to see if I'd get rejected.

I think the point someone else made was great--if you're asking this question, so might a boarder crossing person. In my case, I had been thinking about the damage to my passport for about three trips . .. and got called out on it on the third.