Each square should be 1 movement, diagonals included. It is needless complexity otherwise, and 5-foot movement is an abstraction anyway so it doesn't force me to suspend disbelief any more than I feel is reasonable.
I'm an adult, I'm familiar with Euclid (very cute 3 second google image search btw), and also n-dimensional geometry, and I think that something as paramount as movement through space demands simplicity. The game is more expedient, and fewer mistakes will be made with 1 square = 1 square. I would wager that the majority (51% or more) of DMs miscalculate distances and Line of Sight in 3.5 at least once per session.
If you don't want to get shown up by a computer game, then hopefully your human DM ingenuity and reflexes can effectively/quickly compute distance/area. Is everyone clear on the volume of a cylinder? Surface area of a sphere? Uh oh, it took more than 5 seconds to answer (4)(pi)(r^2) didn't it? Maybe you should look into using Firecubes, otherwise your players will be playing World of Warcraft on their laptops while waiting 15-30 minutes for their next turn in combat.
Infinite complexity is not ideal, quick gameplay is key. 1 square should equal 1 square, and I firmly believe this is the way 4E will work.