Hi,
Comets that swing in close enough to the Sun do eventually fall apart sometimes. I don't know if Halley will or not. It is also possible for them to crash into planets too (see the pictures of comet Shoemaker-Levy hitting Jupiter in 1994 here: http://www2.jpl.nasa.gov/sl9/top20.html), but that is very rare, and we don't expect it to happen to comet Halley.
We are on the lookout for any object like that that might hit Earth. See http://neat.jpl.nasa.gov/neofaq.html
Terry