My personal experience shows that it's best to have no bike paths at all. I typically only use my bicycle as means of transportation here (in Vienna) and the only accidents that I had so far were at locations where the bike path crosses a street. This is also confirmed by statistics.
Compared to this, on streets I almost never have any risky situations - even on busy multilane streets. Cars see you earlier, because you ride on the same street as they do. You don't appear unexpected (for car drivers) because you overtake on the left side like everyone else. The right of way is clear, as there are no exceptions as in the case of bike paths.
In cities such as Copenhagen and Amsterdam bike paths have an advantage, because you are faster (no traffic jams) and because car drivers expect bicycles at crossings due to the high amount of bicycles. In cities such as Vienna where the amount of cyclists is relatively low most car drivers don't expect to encounter them - so even if you have the right of way on a bike path they just ignore it.
I think you are fortunate to live in a place where bicycling is already a mainstream means of transportation. However, in many places in the U.S. (Massachusetts and New Jersey come to mind for me) it's not that drivers are distracted, but rather that many do not believe that bicycles are a valid means of transportation. If you are in the lane you will encounter real hostility and agression. In these cases, I think something needs to be done to reinforce to people that bicycles have just as much right to the roadway as cars. I'm not sure bike lanes are the solution, but something needs to be done to get the number of bicyclists up to a critical mass.
Up in Vermont it has really taken off in the past 10 years. And it is people doing it for recreation, not for transportation.
The problem it seems to me is the size of the roads. Most of the time you can not cleanly get around a biker without going into the oncoming lane. On a 50mph road with bikers going 20mph you constantly have to judge the speed of oncoming traffic to see if you can safely pass or get hard on the brakes to wait. This happens a lot and is annoying.
It's annoying for the driver. It's worse for the bicyclist who has to worry about whether the driver have actually seen him as he comes barreling up from behind.
But yeah, it's true that whoever designed shoulder-less roads was completely clueless to non-automobile transportation like biking, walking, or really even scooters that can't keep up with traffic.
(Incidentally, the "coming up from behind" situation reminds me of one of my biggest annoyances as a motorcycle rider: people who come barreling up behind you when you are stopped at a light and then go hard on the brakes. They are apparently clueless to the fact that many motorbikes are rear-ended at stoplights because drivers fail to note the biker. The net effect is that you need to keep staring at your rear view mirrors ready to take off to avoid getting rear ended in case they actually haven't seen you. Really, the light is red. It won't hurt you to slow down gradually. So please everyone, don't do this.)
Here in Cambridge, UK we have a similar issue and an unusually high concentration of cyclists.
There is a significant effort to install so-called "continental-style" cycle lanes along some major routes. These really are lanes of a decent width in their own right, typically a couple of metres, modelled after the kinds of place you mentioned.
However, the opinion of local cyclists is fairly consistently that if you can't have proper facilities like that, you're better off with nothing at all than with a bit of paint on a normal width road that marks a "lane" barely wide enough to contain handlebars even if you're cycling in the gutter. It is now very clear that such lanes just encourage cars to pass far too close, and drivers to complain when cyclists do crazy things like riding in the main traffic lane because the gutter is full of water/broken glass/etc.
There is plenty of evidence now that having no lane at all actually results in drivers being more patient and giving more space when passing cyclists than having a lane too narrow to be sensible but marking it out clearly.
That works well in dense inner cities, not so sure about less densely populated areas. I think bike lanes work ok when the blocks are long and straight but there's always a problem at intersections.
Also, although shrinking, cars are bigger in the US and drivers seem to be more distracted.
Most close calls I've had were either with seniors, cell phone talkers, distracted moms or young kids, probably roughly in that order.
There aren't too many bike paths in Toronto, or Ontario as a whole. However the law dictates that cyclists have the right to use a full lane if they want to, which is quite great. If you don't feel to comfortable to have cars passing by you so close, then you can take up the whole lane, and they will be forced to overtake you as if you are a car.
Compared to this, on streets I almost never have any risky situations - even on busy multilane streets. Cars see you earlier, because you ride on the same street as they do. You don't appear unexpected (for car drivers) because you overtake on the left side like everyone else. The right of way is clear, as there are no exceptions as in the case of bike paths.
In cities such as Copenhagen and Amsterdam bike paths have an advantage, because you are faster (no traffic jams) and because car drivers expect bicycles at crossings due to the high amount of bicycles. In cities such as Vienna where the amount of cyclists is relatively low most car drivers don't expect to encounter them - so even if you have the right of way on a bike path they just ignore it.