All bicycling advocates with more than half a brain warned about exactly this problem whenever bicycle lanes were put forward as a "solution" in North America.
Personally, I both drive and cycle in urban and rural settings. Unless I'm in a situation where there couldn't possibly be a cyclist on my right, such as an expressway exit, I habitually check on the right before turning right to see if there's anything there. As a cyclist, I think checking for motorists making turns at intersections that could endanger me, is just part of what you have to do to survive.
Having said that, while cycling I've had two accidents with motorists suddenly turning right in front of me to enter driveways. The only logical conclusion is that motorists have to smarten up and take note of the presence of cycists, since in both cases the motorists passed me immediately before they initiated their turns. Unlike what a couple of posters said, the situation can be such that the cyclist just does not have time to avoid a collision -- even if the cyclist is aware of and watching out for exactly this situation. Insurance company examinations of these incidents agreed the motorists were the at-fault parties.
(Naturally the police refused to lay any charges. Typically they won't even consider ticketing a motorist unless there is an injury-producing accident, and they define there is no qualifying injury unless an ambulance attends. Even if they attend the scene and there are witnesses. Therefore close calls, which are more dangerous to cyclists than fender benders are to motorists, receive utterly no consideration from the police.)
If while cycling I have to do a panic stop at an intersection to avoid being struck by a motorist, I will go after them and if I catch them, such as at the next light or in a parking lot, engage them in an "educational discussion". I will even wait for them the next day at the same time and place. I do this because the police have proven that cyclists basically have to take the law into their own hands.
I noticed D70's comment about pedestrians on bike paths. Around Vancouver, it is typical for the bike lanes to be crowded with pedestrians, while the adjacent sidewalk is empty! I don't agree with this, but can see why people do this since in some places the bike lane is wider and paved, while the walking path is narrower and perhaps unpaved. I often wonder if these pedestrians are exactly the same folks who, as motorists, object to cyclists being in their way. Probably.
Shesh, we have such an overwhelming need for education about how to share the roads. Go to Denmark or Holland to see how it should be done.
And while I'm ranting, I'll repeat a point I've made before. You can build all the cycling infrastructure you want, and cyclists won't feel and be safe until they have the full respect of motorists. And they won't have that respect until ALL motorist/cyclist accidents are deemed to be the fault of the motorists. When word gets out that motorists are being really nailed for colliding with cyclists, motorists will start taking better note of the presence of cyclists, and keep their distance. Only this will correct the imbalance between the weight the respective parties are throwing around. But it requires the buy-in of the police, who so far typically represent the interests of motorists.