5 full days...
Day 1: Magic Kingdom. EPCOT is my favorite park, but there's no better way to kick off a Disney trip than at MK. It is special. Make sure you hit Mickey's Philharmagic. IMO, it's the best ride in MK. Stay for Spectromagic and Wishes to end the night.
Day 2: EPCOT. Hit the highlights of Future World (fastpasses for Soarin, hit Test Track, Mission Space, Turtle Talk w/Crush, then see where you are with time) in the morning and early afternoon. Make sure you give yourself plenty of time to roam World Showcase at your leisure. I'd plan on getting to WS no later than 3:00 pm, spending the rest of the evening there to eat, roam the countries and watch Illuminations. Taking your time here is critical in getting everything you want out of World Showcase.
Day 3: AK. If you've never been here before, get fastpasses for Everest first thing, and hit just about everything you can. You should be able to see everything here in a day without really rushing (Kilimanjaro Safari, Maharajah Jungle Trek, Pagnani trail, Dinosaur, Tough To Be a Bug, Festival of the Lion King, Flights of Wonder and Kali River Rapids - if you want to get wet).
Day 4: MGM. This is another 1-day park if you've never seen it. Rock & Roller Coaster, Tower of Terror, Indy Jones, Lights-Cameras-Action, Great Movie Ride, One Man's Dream, Star Tours, Muppet 3-D...and DON'T MISS FANTASMIC...trust me.
Day 5: EPCOT/MK. You might want to reserve this day for after you've had one day in all 4 parks, and decide which one(s) you'd like to re-visit and see something you didn't see before, or want to see again. EPCOT and MK almost always require at least a day and a half if you haven't been there before (or been in a long time), so you could make a day out of hitting both of these again (and it's easy to do that since they're both connected by the monorail).
5 days should be enough - and also make sure to check the closing times in order to get the most out of each day.