It seems like whenever I watch a video of someone playing, his fingers are straight and perpendicular to the top of the fret board. If I put my fingers on any string at, say, the 8th, 9th, 10th and 11th frets, my index finger and pinkie finger will be coming in at about 45 degree angles to the top of the fret board. Even at lower frets, where the spacing is wider, those two fingers are still on angles.

If I'm not clear about this, hold your guitar so that the top is facing the ceiling. Put your eyes level with the top of the fret board, and imagine four fingers on a string on consecutive frets. The first and fourth fingers are tilted out to the left and right respectively, rather than being straight up and down.

The angle makes it more difficult for me to get a clean contact with the fret.

Is this normal, or do I have unusual hands?
Paul Gilbert angles his fingers.

The tendency to angle your fingers is less if you have your thumb behind the neck.

The higher your thumb rides on the neck, the greater the tendency to angle the fingers.

Is it a problem? Not unless it's a problem. If you find it a problem then adjust the position of your thumb on the back of the neck.
Last edited by Virgman at Feb 25, 2015,
both have advantages, angled better for bends, some finger patterns are easier, like skippinga fret between 2nd and 3rd fingers, like the spock hand sign, very hard to do physically with fingers straight. Experiment and see what works where.