Of course it is safest to print out your confirmation as it eliminates any doubt. I am however a frequent booking.com user (mainly due to their easy cancellation policies) and over the past year I don't remember ever needing more than my name, ID, and credit card to check in. I just finished a week Europe trip (July 2013) and that was the case at the 4 booking.com hotels at which I stayed.
So looking at it from a cost/benefit analysis, I'd say you can skip printing if the inconvenience is great (no access to printer, running late for a plane, etc.) or if you have a higher tolerance for risk. My personal approach is the hotel ultimately wants your business, and booking.com generally holds them accountable, so I don't worry too much about not having a confirmation paper.
One caveat: just because you check in does not necessarily mean you get exactly what you expected. If there is an amenity booking.com said you'd get that isn't given, that would be another case where your own printout would help.