For any reasonable mountain bike, it is advisable to keep one finger on each brake at all times. How does this advice transfer to road bikes?
Let us define the parts of the bar according to this answer.
If you're riding in the hoods, you might have your fingers over the brake levers.
If you're in the drops, you're (usually) able to reach them (moreso on newer levers), but you probably don't have your fingers on the brake levers.
On the tops, you probably won't be able to reach the brake levers unless you have interrupter or suicide levers.
Having constant access to the brakes isn't as necessary as it would be in mountain biking (where you're spending a lot of time modulating the brakes; road riding does this very little, primarily to stop, sometimes slow down or clean the rims in anticipation for braking). Of course, you'll pick also depending on the environment -- if you're riding in city traffic, you'll likely ride in a position that you have the best visibility and brake access. Note mountain bikes typically have one position; possibly an additional position via bar ends (unless you have a relatively rare drop bar mountain bike).
You'll choose your riding position according to preference or comfort (switch hand positions for comfort) in many cases, which will dictate your brake access.
While @Batman makes some good points, round here we have some descents on narrow country lanes with high hedges and poor road surfaces. Modulating speed is much more important than on the open road. You might get up to 50 or even 60km/h on a clear stretch but then have to brake for a blind bend. You don't want to rely on braking too hard because of loose gravel or patches of mud on the road. We do also have open road fast descents but they tend to be on busier roads and I won't go into them.
I'm lucky enough to have discs on a tourer and can use continuous light braking at the back to control my top speed, then slow down with the front brake before a bend.
I prefer to do anything tricky on the hoods (these descents, traffic) and can crouch quite low if I do get a nice straight. So I like to have 2 fingers on the brakes as the index finger is very near the pivot - with index and middle fingers I've got all the stopping power I want (subject to road surface). In the drops, one finger is enough because it's got more leverage, but only if I've checked the brifters - when badly adjusted the tab you press when shifting to a bigger cog limits braking when it hits my fingers.
I apply similar methods to other cases when sudden braking might be required, like in traffic (1 to 3 fingers depending on road surface, speed etc.)