There are very few compositional conventions I pay attention to on a regular basis. I try not to cut people's heads off at the top of the frame. When I think about it I try not to crop people at the elbows. I try not to leave big areas of dead space that make a frame look dorky instead of interestingly artful. And I try not to overlay the "golden rule" or the "rule of thirds" on my images intentionally. But one thing that I'm a suck for is diagonals. When I see em in the frame it makes me mash down on the shutter button in an almost Pavlovian way. See diagonal, drool, and then punch shutter.
I like odd compositions but only if they feel right. Diagonals always seem to feel just right.
"If they give you ruled paper turn it sideways." Cervantes.