Why do people say that God denounces the handicapped in the Bible? I often hear people saying that God doesn't like the handicapped etc. 

What evidence is there in the Bible that suggests this? Of course there must be somewhere in the Bible that either directly suggests this or insinuates it enough for people to come to this conclusion.

So what mentions are there in the Bible that are related to the handicapped - I'm mainly looking for negative quotes but the good won't go amiss.
That will depend on who you ask. Probably the most commonly cited passage in scripture is in Leviticus 21:


  16
  The LORD said to Moses:
  17
  Say to Aaron: None of your descendants, throughout their generations, who has any blemish shall come forward to offer the food of his God.
  18
  Anyone who has any of the following blemishes may not come forward: he who is blind, or lame, or who has a split lip, or a limb too long,
  19
  or a broken leg or arm,
  20
  or who is a hunchback or dwarf or has a growth in the eye, or who is afflicted with sores, scabs, or crushed testicles.
  21
  No descendant of Aaron the priest who has any such blemish may draw near to offer the oblations of the LORD; on account of his blemish he may not draw near to offer the food of his God.
  22
  He may, however, eat the food of his God: of the most sacred as well as sacred offerings.
  23
  Only, he may not enter through the veil nor draw near to the altar on account of his blemish; he shall not profane my sacred precincts, for it is I, the LORD, who make them holy.
  24
  Moses, therefore, told this to Aaron and his sons and to all the Israelites.
  (Leviticus 21, NAB)


This passage forbids Aaron and his descendants (who were given priestly responsibilities) from approaching God if their bodies were blemished in certain ways. Some of these blemishes would permanently deny this aspect of the priesthood to those people who had them:


permanent blindness
permanent lameness
dwarfism
uneven limbs
crushed testicles


The passage does not specifically identify the reason that God considers these blemishes to profane the altar of the temple. As far as this passage goes, “God doesn’t like the handicapped” is only an interpretation.