I think, a defaultsized character taking up 3x3 tiles by default would make things a lot of easier.

Also, since I was doing both prerendered 2D and 3D isometric games, I recommend 3D. Really, prerendered 2D iso tiles is "passe" technology, not that easier, harder to produce assets, problems with dynamic lights. With 3D iso (if you don't need partial transparency) you just drop objects of any size in any order and enable depth buffer :)

I liked A Link to the Past's system(Although it is an action game). The world is built on a grid the same size as Link, but he can move in increments of half a tile. It makes it obvious where he can walk and where he can't and building the maps should be easy, but at the same time his movement feels very free. I had to check on my emulator to see if he actually moved on a grid at all. Diagonal movement looks kind of natural too.

To me, ledges and cracks are bonus features for the eager programmers and animators but having units of different sizes and shapes is a real issue.

I think 1x1 suits slow paced/turnbased games with lots of units and tactics and 2x2 *might* make more sense in faster/semi-turnbased games and games with fewer units.

"I think, a defaultsized character taking up 3x3 tiles by default would make things a lot of easier."
Why is that? Or are you luring me down the path to gridless games?

I have to confess that I'm not making a specific game and that's why I'm so vague. I'm just trying to learn more about the theory and think about how and what I want to make. And I love brainstorming.

I discussed your idea at another place and mentioned my 3x3 suggestion there too, and I got a quite similar "Why not just going gridless then?" :)

I just think a lot of things are easier to code when there is a center cell, and it is easier to parse for the players' eye, when characters are not sitting between the cells all the time. But that has to actually be proven, maybe it works out well. I'd start with a simple prototype, I guess.