As I write, I'm busy installing Unity on my computer. Up until now, every single one of my games have been two-dimensional. Although I have a few abandoned projects with 3D graphics, I have only ever coded in 2D.
If you already know and love 3D, you'll be able to back me up on some of the following points (and, likely, disprove some of them, since you have more experience of 3D than me). Regardless, I'm going to explain what appeals to me about 3D game design. (Some of my points don't apply to all genres; although I am used to creating platformers, I appreciate that top-down games are equally common, and solve many of the problems described below.)
First: The basic topology of 3D space. Simply put, 3D gives the player two extra directions he can go in, which while totally unsuitable for linear platform games, is perfect for more open-world games. A 2D world map is less complex than a 3D one. A 2D platformer which refuses to include ladders and improbably placed staircases (such games are few) limits the player to only going left and right, or entering a building. This may be desirable in the case of fighting games and reflex platformers, but it is annoying for an exploration-based game (and one of the reasons An Untitled Story has teleporters scattered around the map).
Second: The view range. 2D can only ever show a small area around the player, or risk making the details too small to make out. The only way the player of a 2D game can see the entirety of an area is by looking at a map or by walking through the entire place. Furthermore, it is impossible to hide objects from view in 2D (for instance if the player needs a key to open a door, it will still be possible to see for some distance on the other side of the door before it is opened). 3D enables level designers to give the player a complete view of a wide area very easily, not to mention that locked doors remain opaque.
Third: Beautiful graphics. I appreciate this is highly subjective, and not something I am likely to achieve in 2D or 3D, but 3D enables jaw-dropping views to be inserted into the game without interrupting gameplay. I don't mean to say that 2D games can't be beautiful, just that 3D games are much better suited to introducing panoramic views of the environment.
Fourth: 3D is simply more realistic. Games that bank on their realism (once again, not mine) are 3D by necessity. Many things are nearly impossible to represent in 2D, yet we see them many times in our daily lives: for instance, a corridor with 3 exits on the same floor, or a wall which is a different colour on each side.
I am not saying that 3D does not have disadvantages, I am not saying that 2D games are incapable of overcoming those disadvantages that apply to them, and I am certainly not saying that 3D is better than 2D. 3D requires a much greater investment in graphics and level design, consumes much more processing power and memory, and is totally unsuited to many games anyway. Many puzzle/arcade games require the player to be able to view the entire area at once, which is much easier in 2D. 2D also makes it much easier for the player to see any secrets, Easter Eggs, or extra areas that may be in the game (recognising them is another matter).
What I am saying is that 3D forces a completely different set of design choices from 2D, that games created in one dimension will often not work in the other, and that I want to try making something totally different from what I have made before. I don't know what will happen, but I hope it will be fun for all involved.
