You'd usually whirlpool and/or have some sort of screen to prevent excessive trub and hop particle pickup. The effect of trub in the fermentor is relatively minor, but I personally prefer a clean wort going into the fermentor because plate chillers are a bit of a pain to clean. I currently Whirlpool for 30 minutes using a pump that recirculates wort through my crappy generic plate chiller (by starting the pump with 10-15 minutes to go in the boil, it also sanitizes the lines and the chiller), let it settle for 15 minutes, and then very slowly run off through my Hop Blocker and plate chiller into the fermentor.
The Fiesty(sic) Goat Brewery est. 2007 & Clusterfuggle Experimental Ales est. 2009
Planned: sLambic II, Flanders Red II, Orange Blossom Mead, Fat Man Porter
Primary:sLambic I, Janet's Brown
Secondary: Toasted Caramel Port, Flanders Red
Kegged: Hefeweizen, Centurion Falcon IPA< Dark Saison
2013 dump volume: ~2 gallons