I don't cover mine, because an immersion chiller works best if you stir the wort every few minutes.
but I also chill in the kitchen, with teh room closed off from dogs (no kids) so the chance of something falling in from above to contaminate is almost nil.
haven't have a problem yet.
Primary: English Mild
On tap: Pale Ale, Lancelot's Wheat, English Brown Ale, Steam Beer, HoovNuts IPA
Bottled: MOAM, Braggot, Raspberry Melomel, Merlot, Apfelwein, Pyment, Sweet mead, Cabernet
Gal in 2009: 27, Gal in 2010: 34, Gal in 2011: 13, Gal in 2012: 10