I use a generic plate chiller that I haven't been particularly happy with because it takes too long to chill with the high ground water temps here in Florida, but I haven't had any problems with it clogging. I whirlpool/recirculate with it starting at 15' remaining in the boil, all the way down to ~85-90 degrees temp. Right now it goes through a Blichmann hop blocker; before that, I used a Kettle/Bazooka screen as well as hop socks. They are impossible to clean perfectly, which is why running boiling wort through them is important for sanitation.
I did have to pull out my immersion chiller for my pumpkin ale I brewed on Tuesday, but that was only because the pumpkin clogged the hop blocker and prevented flow to the pump, which I kind of expected.