It's funny you should mention Toy Story. Pixar's John Lasseter is well known to be a friend of Miyazaki. Studio Ghibli even released a DVD of the home movie visit to America titled Thank You, Mr. Lasseter.

http://www.nausicaa.net/miyazaki/lasseter/

I remember seeing once that Pixar had a life size Cat-bus from Miyazaki's Totoro installed in their studios.

The original home movie DVD release of Spirited Away was also introduced by Lasster.