Sorry about the poor quality of the image below. I took it on the spur of the moment, using an iPhone, on Saturday when we were stopped at a red light that has annoyed me for years. If I can get a better picture sometime this week I will edit this post. This light is at the westbound end of Eisenhower Avenue at Van Dorn Street in Alexandria, Virginia. There are four lanes on Eisenhower and we were in the leftmost one at this point, a left-turn-only lane onto southbound Van Dorn. There are two right-turn-only lanes and a left-or-straight lane; the light for our lane is out of the picture to the left.
The thing that annoys me at this intersection is the combination of the traffic lights and that white sign that's visible. It may not be apparent from this image, but the two right-turn lights use red arrows. Then there is that small white sign up there. It says "Right Turn on Red from Curb Lane Only." (Those of you who drive in Virginia no doubt know that VDOT is obsessed with this issue and usually posts signs for the second lane from the right using some variant on the phrase "No Turn on Red This Lane.")
The issue at this intersection is—why have a red arrow at all if you're allowing turns on red? I like the idea of the red arrow for the second lane, from which turns on red are prohibited, and I think it would be a useful tool at other intersections, especially because out-of-state drivers aren't always aware of Virginia's prohibition on turns on red from other than the curb lane and because at large intersections the small white sign is sometimes hard to read (especially at night). But at least across the river in DC the red arrow is normally interpreted to mean that you cannot go in the direction of the arrow until you have a green light—that is, the red arrow seems like it should be a prohibition on a specific movement along the lines of "even if there is a green light, you cannot turn in this direction right now." Doesn't allowing a turn on red defeat the purpose of a red arrow?
(Virginia's statutes allowing right turns and left turns on red do not specifically speak to red arrows—they just say that "vehicular traffic facing a steady red signal" may make a right or left on red after stopping unless a sign prohibits the maneuver.)
What is the rule elsewhere around the country? Off the top of my head I can't think of any other red arrows in Virginia, but they're pretty common in DC.