Interesting thread, I've just started a thread about a proposed remake of My Fair Lady so this is right up my street.
Good Remakes
Planet of the Apes
Good sequels
Empire Strikes Back - if only for the, "I am your Father" line (I can still recall my 12 year old jaw dropping and the collective intake of breath of the entire cinema when this little gem was revealed!)
Bad Remakes
Too many, but a few that spring to mind are Cape Fear, Psycho and Hairspray
Bad Sequels
Again too many but some I could single out are Attack of the Clones (not strictly a sequel, but you know what I mean), Shrek 3, all of the Halloween sequels.......I could go on all day