Kind of a reiteration of what other's have posted. For me. If I have to turn right at an intersection. And on the street in front of the light has one of those arrows where one goes straight and the other turns right and there is ONE car waiting at the light then I will go between said car and sidewalk or parked cars to take a right turn on red. And yes, I do keep to the left if I'm in the right lane so that cars can turn right (hope that didn't sound confusing).
I asked a police friend of mine and he said it's okay to do but if there is more than one care in front and I try then it's illegal. Do different states have different rules on this? I know for instance, NC is one of the few states you cannot take a left turn on red when entering a one way street.
Quick story, Going to work at 6am about a month ago came to the usual single lane stop light intersection right before I enter my work place (just like the one described above). No cars around except the one in front. Light was red. For some reason, the lady stopped more than a car length from the line. Left blinker on. I'm turning right so I filter between her and the parked car. Plenty of room between us but still cautious. Sure enough, I get the honk. First time I ever had that happen so I just stopped, turned around, and pointed to the pavement arrows, and continued on. I guess she thought I wasn't being safe or I was doing something illegal. Meh.