Okay, diagonal movement being equal to horizontal/vertical movement bugs me, hard. I know it doesn't bug alot of you, but it bugs me.
For one thing, it makes most impediments to movement meaningless. If you have obstacle X between you and target Y, it costs absolutely nothing to simply go around it via diagonals. Moving in a zig-zag down a hallway is identical to moving straight down it. There's a mountain. A tunnel goes through the mountain. It is exactly as fast to go around the mountain than to go through it. MADNESS!
And so I propose two simple homebrew rules to fix this problem.
1. Diagonal movement costs 1.5 squares of movement. Diagonal distances are 1.5 as far when considering the range of powers and the area of effect of burst powers.
2. The distance of all move actions is increased by .5. The range of all powers is increased by .5. The area of effect of all burst powers is increased by .5
So, for example, the legal movement of a character (x) with a movespeed of 6, under vanilla D&D looks like this:
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ x ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
Under these houserules, it looks like this:
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ x ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
As close to a circle as you'll get without a ruler determining range.
For situations where an enemy soldier (o) is between you and a target you wish to get into melee range of (t), this is what it looks like in vanilla:
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ x ♦ ♦ o ♦ ♦ ♦ t
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
The green diamonds are squares you can only enter by moving adjacent to the obstable, provoking an opportunity attack from it. It's insane, the "obsticle" does nothing, you don't even have to go near it!
This is what it looks like with this houserule:
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ x ♦ ♦ o ♦ ♦ ♦ t
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
Still possible to become adjacent, but the obstacle requires you to skirt it, and you are vulnerable to an opprotunity attack.
A more signifigant obsticle than an enemy soldier would be a wall: even a 25 foot long wall is utterly IRRELEVANT under the vanilla system:
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ x ♦ ♦ o ♦ ♦ ♦ t
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
You can skirt the whole wall because of the way the game deals with movement. Under the houserule, it looks like this:
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ x ♦ ♦ o ♦ ♦ ♦ t
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ o ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦
A wall actually inhibiting movement? Wow.
Actually, you cannot 'cut corners' if there's an object that fills the whole square present.
So you do have to indeed go around walls, for a bit at least.
Also these rules don't count outside of combat so the mountain/tunnel story doesn't work.
Other then that, the rules appear to be ok, if it really starts to bug me I might start trying them out 
The classic movement counting from 3rd Edition. The reason they went away from it is because it made counting movement clunky. It's considerably easier to count "1, 2, 3, 4..." than say "1.5, 2.5, 4, 5.5..."
I'm not saying it's better or worse, but I know I like keeping movement simple, even if that results in Fireball becoming Firebox, so it's really an each-to-their-own issue. Just make sure to take all consequences of this house-rule into considerations.
As for the wall example above, try counting where the wall provides "hard corners" you can't move past diagonally.
My group just played the whole of KotS intro adventure effectively with this house rule, because we didn't notice this had changed between v3.5 and v4.
It was fine. We didn't alter the shape of bursts and blasts (we found those in PHB OK :-)
I am considering whether to re-introduce RAW for 4E in this regard, now it's my time to DM. The RAW makes it quicker to count moves, but yes it does mean that certain terrain features behave "odd", especially at a moderate battle scale. It tends to be a problem when you have some feature perhaps 3x3 or larger, with also enough space near it that moving diagonally is an option.
If you want a specific tactic choice in an encounter such as "risk going through shortcut region A, OR take safer longer route B" then you can set it up on the map. The issue still remains that ad-hoc situations like this (perhaps a conjuration zone, or some other characters in a melee) can often be solved by zig-zagging.
In balance though I'm probably going to introduce the RAW, for speed.
First, how does this affect shifting? Can you shift diagonally if moving diagonally costs 1.5 movement and you can only shift 1?
How will you handle 3D movement? Mathematically, moving diagonally on a 2D (forward and left) grid is 1.41 movement. Moving diagonaly 3D (forward, left and up) is 1.73.
I simply count every second diagonal move as two squares. Same for calculating range (Diagonal movement through difficult terrain is always three squares and two squares for lateral moves).
Another option is to double all reference to distance and range in rules and powers and make the cost of lateral movement 2 "squares" and the cost of diagonal movement 3 "squares". That makes counting very easy (2-4-6-8...) (In difficult terrain, lateral moves would cost 4 and diagonal moves would cost six).
I haven't used the second system though but it should work fine -- if you can get past the notion that a "square" costs 2 or 3 "squares" of movement.
The half-square can be a real pain. In 3.5, you'd count every second diagonal as two squares, but that screws things up, when something that's counted one way comes up against something that's counted another. :shrug:
Another alternative is to ditch the grid and measure things. That's the way wargamers used to do it. Felt tables with terrain models and miniatures on it, and string and tapemeasures to determine range and the like. It worked.
I do find 4e geometry to be amusing though. Try this experiment. Have one character hold one end of a 10' long rope, and another hold the other end. Have the second character pace in a 'circle' around the first, keeping the rope taut. Notice the shape of the circle.
Try inscribing a circle in a square or vice-versa. ;)
Back when we played in 3.5, I almost immediately switched over to hex grid maps over square grids. This decision influenced almost entirely by Unearthed Arcana.
We'vebeen trying the new non-euclidean grid for over a dozen sessions right now and so far it hasn't been a problem, but I could see myself going back to the hex grids soon.
In fact, you can still apply all the normal 4e movement and area rules within a hex grid and it will automatically shift into something that not only looks more natural, but is still easy to work with.
I've worked it out. In a hex grid, with 4E's rules:
diagonal movement is just normal movement,
all maximum ranges from a center always form a circle,
a close blast affects less targets but you are also being surrounded by creatures so it balances out,
a wall can be done on several more angles adding needed flexibility,
bursts look like circles and blasts look like cones,
a burst 1 goes from 9 squares to 7 hexes,
a blast 3 goes from 9 squares to 6 hexes.
That's just off the top of my head, but you can see there is an advantage in hex grids. For now, we'll still hang onto the square fireballs, but I'll soon be asking my players if they want to go back to hex.
Hex is pretty good, but it has its own problems. For one, six directinal movement is less natural to humans than eight directional. Secondly, 3d becomes a HUGE pain. As well, the entire dynamic for flanking changes, as there are less ways to score a flank. Not to mention the other things that this effects, like lowering zones of control.