At night I run my handlebar mounted headlight and helmet mounted headlight constantly on. On the back I run my rack mounted taillight constantly on, my seatpost mounted taillight, a Cateye TL-LD1000, with one bank constant on, the other bank in flash mode, and my helmet mounted taillight constantly on.
During the day in overcast, foggy or rainy conditions I add a handlebar mounted headlight and run it in flash mode, with both banks of my TL-LD1000 in flash mode.
Flashing lights are an attention grabber, but do nothing for spacial awareness. With nothing to compare it to, the viewer of a flashing light in the dark cannot tell if the light is moving nor how far away it is. With a single light that is constantly on the viewer may be able to see the light moving, but will have nothing by which to judge distance until they get very close. Multiple lights that are constantly on make judging movement and distance easy. That is why I run two headlights and effectively four taillights at night. During the day under low light conditions I can be seen easily enough, I just want something that grabs the attention of motorists and says, "HERE I AM! SEE ME!", so that they notice me earlier than they otherwise would.
It has been my experience that I am seen and noticed earlier during daylight conditions that I run flashing lights, than I am on bright, sunny days without the lights.
When towing a trailer I usually remove the rack mounted taillight in favor of a taillight on each rear corner of the trailer, effectively giving me five taillights. The trailer mounted lights are run constantly on.
Another reason I think running multiple lights is important is you never know when one is going to malfunction or, especially in the case of taillights, bounce off.
Am I worried about blinding others? Not really. My headlights are much less intense and cover less area than those of a car. My handlebar light is aimed at the road as far out as I can still have the hot spot on the asphalt. My helmet mounted headlight is, of course, aimed where I am looking, but if I don't want to blind someone I just don't put it in their face. The flashing headlight that I use is mounted to aim straight ahead to be the best noticed by motorists, but I only use that one during daylight.