Are all animals right or left handed?

Now for something completely different - a video sequel to Basil's Book Launch plus a question for zoologists, ethologists or anyone else who might know about such important matters.

However noisy and irritating Basil's impatience may be when demanding (yet again) to be fed, he is utterly consistent in one notable thing: never have we seen him using his right paw to rattle the dish.

So the obvious question is whether or not this is 'normal' and, more generally, are all cats and other animals right or left-handed/pawed?

P.S. Apparently most cats are left-handed

Thanks to Lisa Brathwaite (@LisaBraithwaite) for tweeting news from a vet in California suggesting that Basil is not, as we'd suspected, unusual in preferring his left paw.

She writes: "Our mobile vet told us the other day that most cats are left-handed. We have one who pats us for attention; always left paw" (7th March, 2012).

Further inspection reveals that Basil also uses his his left back paw for scratching himself during a rest from rattling his dish: