Considering a medium creature, with 5ft of reach, wielding a reach weapon such as a longspear.
By the rules:
With a typical reach weapon, you can strike opponents 10 feet away, but you can’t strike adjacent foes (those within 5 feet).
Squares within 5 feet would be all adjacent squares to the creature, including diagonal ones (first diagonal being counted at 5ft).
It appears clear that the weapon will allow attacks into four squares: those 5ft away from the creature in the north, east, south and west directions. They are 2 squares away in a straight line, thus 10ft away, within reach.
But now, what about the squares diagonally away, beyond 5ft, north-east, south-east, south-west and north-west of the creature? According to the rules, the second square of a diagonal line is considered 15ft away when it comes to movement. Does this also apply to attack distances?
Also, what about squares reachable by going diagonally once, then straight up/down/left/right? This would usually count at 10ft of movement, so are they attackable?
Here’s a diagram:??X????XCX????X??
C is the creature, blank spaces are where I assume you cannot attack, Xs are where I assume you can attack and ?
s are where I’m not sure you can.
In searching for answers to this, I’ve come across an interesting point on the Paizo forums. If you are in one of the far corners and you consider these not threatened, then you can diagonally move towards the character and never provoke an AOO (that is, per RAW)… and yet, logically, a threatened area should make an uninterrupted circle around the creature. This may explain why 3.5 made an exception out of this.
You lose some corners for longer reaches.
The lavender-and-green graphics toward the bottom of this page exactly illustrate how reaching on a diagnonal works.
In reference to the FAQ comments by James Jacobs and Sean K Reynolds, I believe they are 100% compatible with this diagram:
Jacobs answers the question “Can one attack someone 15′ away on a diagonal?” Answer: No.
Reynolds answers the question “Does that means one can sneak in on the diagnonal, somehow moving from 15′ away to 5′ away without passing through intervening space?” Answer: Also no. You still trigger an AoO as you pass from 10′ to 5′ away, even though there isn’t a square for 10′ away on the grid.
Regarding differences for creatures that’re long instead of tall, the lavender-and-green reach charts toward the end of the page give examples of both. Essentially the only difference is that long creatures tend to have less reach than a tall creature of the same size.