Toys coming to life is not an uncommon story line. In addition to the Velveteen Rabbit, other well known ones are Winnie the Pooh, The Indian in the Cupboard, and even The Nutcracker.
However, the direct inspiration for the Toy Story movies was not The Velveteen Rabbit. The initial spark was an earlier Pixar short, Tin Toy.
Pixar, who had been producing short animated films to promote their
computers, was approached by Disney to produce a computer animated
feature after the success of the short Tin Toy (1988), which is told
from the perspective of a toy. An agreement to produce a feature film
based on Tin Toy with a working title of Toy Story was finalized and
production began soon thereafter.
Many ideas from an un-produced TV special sequel to Tin Toy, made it into the Toy Story films.
Pixar hoped that this TV special would allow them to work their way up
to make a feature length film one day. However it turned out they
couldn't get the budget to start production on it after the network
refused to give them the right amountof money. The idea was shelved
for two years...until the company was hired by
Disney to make them a full length movie. The story was re-worked until
it became what is known as Toy Story. Some of the ideas from this
un-produced TV special were used for all three Toy story movies.
Disney did not like the initial Toy Story treatment and Jeffrey Katzenberg suggested they look to make more of a buddy film with the main characters that start in conflict and have to come together.
Disney film division chairman Jeffrey Katzenberg felt the original
treatment was problematic and told John Lasseter to reshape Toy Story
as more of an odd-couple buddy picture, and suggested they watch some
classic buddy movies, which include The Defiant Ones, in which two
characters with different attitudes are thrown together and have to
bond.
So once it moved from concept to reality, Toy Story was more influenced by 48 Hours, The Defiant Ones, The Odd Couple and Midnight Run.
The main characters were inspired by John Lasseter's own childhood toys, and went through many iterations before alighting on the final Woody and Buzz.
Woody and Buzz Lightyear are inspired by director John Lasseter's own
childhood toys. He based Woody on his own pull-string Casper doll, and
once he grew out of Casper he moved on to a G.I. Joe, a flashy toy at
the time of his childhood.
The script went through many changes before the final version. John
Lasseter decided Tinny was "too antiquated", and the character was
changed to a military action figure, and then given a space theme.
Tinny's name changed to Lunar Larry, then Tempus from Morph, and
eventually Buzz Lightyear (after astronaut Buzz Aldrin).