What is the best 32bit hash function for short strings (tag names)?

I’m not sure if it’s the best choice, but here is a hash function for strings:

The Practice of Programming (HASH TABLES, pg. 57)

/* hash: compute hash value of string */
unsigned int hash(char *str)
{
   unsigned int h;
   unsigned char *p;

   h = 0;
   for (p = (unsigned char*)str; *p != '\0'; p++)
      h = MULTIPLIER * h + *p;
   return h; // or, h % ARRAY_SIZE;
}

Empirically, the values 31 and 37 have proven to be good choices for the multiplier in a hash function for ASCII strings.