It would be cool if we could move diagonally on islands, making covering the islands more efficient. Because it is a bit frustrating (to someone impatient like me) that we have to press two different arrow keys seperately to get to a square diagonally of you...

Probably could do this by pressing two arrow keys at once? (For example, pressing up and right to go diagonally/northeast)

EDIT: Yes, I sort of agree with what DragonSage says about making this easier, so instead, we should not be able to go around corners (places where we could not go by pressing the two arrow keys seperately)
Also, if pressing the arrow keys at the same time doesn't work , there could always be the arrows on the screen that you click...

I don't support, because a diagnal move would make it easier to avoid some of the monsters while collecting resources (plus I could see too many people saying the keys didn't work because they didn't press the keys simutaneously)

This could work if they made use of the numpad. 7913 would be the diagonal keys.

HOWEVER, I don't think this will or should make it in the game though because of how small islands really are and how this could make it possible to get to some resources and/or treasure chests without defeating the guardian.

In order to accomodate this the islands would need to be generated without any possible diagonal gaps over water - something which is currently very commonplace. Again, re-coding the island generation script would be a time intensive process for little enefit to the game.

no support cause of the fustration for people that have notebooks/netbooks/some laptops that dont really have a numberpad to use.

and like irrimn said the islands themselves would be abused by this

the coding behind this far outweighs the NEED of somthing like this (not that there is a need)

This would be really convenient, but as koben mentioned it doesn't make sense to have it only for number pads--I use a laptop and it has no number pad, so that would be completely usless to me. Personally, if we're talking about island exploration tweaks, I'd rather see keyboard commands for battles than this, but if it's an idea that others want, I'd prefer it to be a clickable button or a keyboard configuration that everyone/most people have access to.

No support for exactly the reason Irrimn said, the map generation isn't built to support being able to move in that way. There are numerous times you could bypass guardians to get to chests doing this.
With it's grid-like generation, I feel it would be unnecessarily difficult to rewrite the random generation code just to accommodate being able to move diagonally.

Perhaps it could be written to tell if one tile within the 2x2 square area you are crossing (one corner to another) is water, that may be more simple, and just not allow that move.

Still, I don't think it's necessary to be able to do that. I'm more apt to support things like entirely automated exploring to save time.