In general, bike lanes (and other bike facilities) appear to be safer. Of course this is not always the case, but the general trend is that bike facilities, including lanes, tend to improve safety in the cycling environment.
One study from 1997 by the Transportation Research Board,
Major streets without bike facilities are where the most bike crashes happen, followed by minor streets without facilities, bike paths, and then bike lanes.
Another one by the Environmental Health Journal in 2009,
A review of 23 studies on bicycling injuries found that bike facilities (e.g. off-road paths, on-road marked bike lanes, and on-road bike routes) are where bicyclists are safest.
On-road marked bike lanes were found to have a positive safety effect in five studies, consistently reducing injury rate, collision frequency or crash rates by about 50% compared to unmodified roadways [61,62,65-67]. Three of those studies [61,66,67] found a similar effect for bike routes. One study  found that there was an increase in crash rates in the year following installation of marked bike lanes on a major road, especially for a section counter to on-road traffic flow, but this effect was not sustained over the long term.
Although the effect of infrastructure design on cyclist safety was first studied more than three decades ago, the literature on the topic remains remarkably sparse. This review highlights opportunities for more detailed and controlled studies of infrastructure and cycling injuries.
Another from Pub Med in 2011,
...Results. Installation of bicycle lanes did not lead to an increase in crashes, despite the probable increase in the number of bicyclists. The most likely explanations for the lack of increase in crashes are reduced vehicular speeds and fewer conflicts between vehicles and bicyclists after installation of these lanes.
Finally, a memo from the New York Mayor's Office in 2011,
When protected bike lanes are installed, injury crashes for all road users (drivers,
pedestrians, cyclists), typically drop by 40 percent and by more than 50 percent in
Based on personal experience, I think that bike lanes are safer when well designed and maintained. I normally use available bike lanes in my city; however, with the caveat being that I make every attempt at maintaining awareness of the surroundings. I'll just say that bike lanes are pretty much useless for the oblivious cyclist; otherwise bike lanes are a good idea.
Observations (so my personal opinion):
- Bike lanes and paths are more or less dangerous depending on the location. Some cities/countries have good cycling infrastructure and some do not.
- Oblivious cyclists are always in danger. So, there's a point to be made that cyclists need to be highly attentive to conditions at all times.
Bikes Belong has links to a plethora of bicycling research and statistics.