Intersections are easily the most dangerous place for both bicyclists and motorcyclists. The smaller vehicles are harder to see, especially for attention-deficit drivers who are distracting themselves with phone calls, etc. Far too often, the motorist laments, "I didn't see him!" after smashing a rider, even though they were often headed straight toward one another.
Bicyclists are also vulnerable to the "right hook" at intersections. The rider is coming up beside a car on the right - in the bike lane, and the right-turning car - often without signaling - turns into the cyclist's path.
(Personally, I'm very aware of the potential for such a situation, and watch turn signals closely. It is required by law to signal a turn, you know. However, I don't trust the non-signaling driver and make sure I have an escape route... just in case I'm suddenly being right-hooked by somebody who can't operate the turn signal on account of the phone, the coffee cup, etc.)
Traffic engineers are always trying to figure out ways to make intersections safer. In Portland, they've tried bright green "bike boxes" - painted pavement to designate places where a bicycle should be. Unfortunately, that particular effort may not have had the desired effect - this story says right-hook accidents have actually increased following their implementation at "a handful of tricky intersections."
Here in Boise, they've kinda done a "Bike Boxes Lite" treatment - some bike lanes have been painted dark green, apparently in an effort to remind motorists that they are sharing the pavement with cyclists. (I hope they got a good deal on the paint, because it's ugly! And it's so dark it's hardly noticeable... and 2 or 3 months later it's fading badly.)
My friend and correspondent Bob T sent me some very interesting info about the Dutch way of doing intersections. Very innovative! (I've never been to the Netherlands, but they are arguably the most bike-friendly folks on the planet. Cycling is part of the "national identity," and bike transportation is routine for the citizenry.)
The intersections are enlarged to create a "semi-roundabout" for the bike lanes, which are isolated from motor traffic by a raised island. Woe to the poor motorist who strays too far to the right - he'll be jumping a curb! The main advantage is improved line-of-sight... motorists and cyclists aren't creeping into each other's blind spots. And of course, as Bob points out, there isn't an "us versus them" attitude of resentment between motorists and cyclists. They're just members of the "family of man" trying to get from Point A to Point B.