Puppies and kittens can be spayed when they are very young.  Many veterinarians are now performing early spay/neuter on animals as young as 6 to 8 weeks.   Studies have shown that early spaying/neutering is safe and results in no significant health differences than animals that were spayed/neutered at an older age.  An added benefit is that animals altered at an early age seem to recover more quickly and painlessly than those altered later in life.