So I was experimenting with half-blocks and stairs, and made this structure:
and since I was inside it when I placed the last stair, I found that I was trapped.
This surprised me since the space inside the structure is 2 blocks tall and 2 blocks wide, and the gap between the stairs in the corner looks quite large. Doing some basic geometry, it's clear that the gap is 1/sqrt(2) or a little more than 0.7 units wide (where 1 unit is the width of one side of a block). It is already obvious that Steve can fit through a 1 unit wide space, but noticing also that doors have width(thickness) and Steve can still fit through the space in an open door seems to imply that Steve's width is somewhat less than 1 unit but more than 0.7 units. I've checked out the Minecraft Wiki and did not find anything detailing this aspect.
How fat is Steve (and the other Steve-sized mobs)?
Edit:
I did a bit more research and found that doors take up 3/16 pixels of 1 unit, leaving 13/16 or 0.8125 units of space that Steve can fit through, with some wiggle room left. This can be seen in the following screenshot:
So the range now is 0.7071 < Steve < 0.8125.
Best Answer
Put Steve in a 1x1 hole and measure the wiggle room. ALL the room - WiggleRoom = Steve
In a 1x1 hole, I pointed the camera straight down and moved from corner to corner. Regardless of corner or orientation, the crosshairs pointed at the farthest point of a 5x5 square from the corner.
16 = 5 + 6 + 5
That's 16 total square width, 5 for the each side of Steve, and 6 for the wiggle room.
Front/back/left/right, the closest you can get to a wall is 5. This test is unable to confirm if Steve is 10x10 square, or a 5 radius circle.
Note: this finding contradicts the original question, as Steve is 0.625 wide, and the asker was expecting more than that. However the original question also supports this answer in the door screenshot (5 texture pixels from door).
It seems reasonable to think that Steve is an unrotating 0.625x0.625 square, which is 0.88 from corner to corner, and could not fit through the ~0.7 gap.
Here is Steve (in green), blocked by two stairs (in purple). Steve is 10 units big, but the yellow line is ~14.14 units big, which is too large to go through the ~11.3 unit opening.