Okay, here's the deal. Tonight, I measured all around the perimeter of the house where there were gutters. From the end of the upper lip of the "drip edge" (see image for what I think the drip edge is) the shingles, on average, extend an extra 3/4" of an inch. In the back of my house, where I have concerns of water coming-in the basement, there's about 2 1/2" max space from the edge of the shingles to the inside edge of the gutter (see picture with my hand) which makes it a tight fit to get my hand in. To be sure, it's less space than what was available prior to the new roof.
On the drip edge, I measure from the back of the piece (what I think is the "fascia") to the extended lip of the piece (looking from the side it looks like an inverted, capital L), this measures about a 1/2".
So, on average, the shingles extend a full inch from the fascia, including the drip edge.
This is what's under the shingle, what I think is the "drip edge". The shingles extend 3/4" past the end of the upper lip of this piece.
Hand gives perspective of about 2 1/2" inch clearance.
Sorry I couldn't get better pictures. I worked late and had to scramble to get something at all before the light left.