Depends on many factors such as crowds for the day, weather, time you arrive, what rides and shows are open, whether you want to do just rides or just shows, do you want to do the big thrill rides or not, stop and admire the scenery or not, want to eat there etc It all depends on you and the people you are with to give an accurate answer. If you want to watch the fireworks and Fantasmic you'd have to stay all day anyway.
If you arrive at rope drop, you can easily get most of the park in by 1pm. If you arrive in the afternoon, you are looking at a much more substantial wait for Toy Story, RnRC and Tower of Terror.
I would dedicate a whole day but as rough estimate, but 6 hours should be more than enough, with moderate crowds that is.
Great Movie Ride - 22 Minutes Long - 10-30 Minute Wait
Muppetvision 3D - 15 Minutes Long - 0-15 Minute Wait
Rock N Rollercoaster - 1:22 Minutes Long - 40-60 Minute Wait
Star Tours 2 - 4:30 Minutes Long - 10-40 Minute Wait
Tower of Terror - 4 Minutes Long - 20-60 Minute Wait
Toy Story Mania - 6 Minutes Long - 60-120 Minute Wait
Star Wars LB - No Fixed Length - Unknown
One Man's Dream - No Fixed length - 0 Minute Wait
Beauty and the Beast - 20 Minutes Long - 0 or 120 Minute Wait
Little Mermaid Show - 17 Minutes Long - 0-20 Minute Wait
Disney Junior Live - 24 Minutes Long - 0 or 60 Minute Wait
Frozen Singalong - 30 Minutes Long - 0 or 60 Minute Wait
Indiana Jones - 25 Minutes Long - 0 or 120 Minute Wait
Fantasmic - 30 Minutes Long - Arrive 60-30 minutes before show start
Star Wars Fireworks - 15 Minutes Long - Arrive 15 Minutes before show start
Character M&Gs - 2 Minutes Long - 15-30 Minute Wait
Citizens of Hollywood -15 Minutes Long - 0 Wait
Jedi Training Academy - 20 Minutes Long - 0 Wait
Attractions closed in the last few years:
-Backlot Tour
-American Idol Experience
-Lights, Motors, Action
-Sounds Dangerous
-Magic of Disney Animation/Animation Academy/Characters
-Legend of Jack Sparrow
In all seriousness, Backlot tour is really the only casualty.