In France, yes. There's a service called "SOS Medecins" that you can call, and a doc can come and visit.
It is overpriced of course (three times what you'd pay at your regular doc, and it won't be completely taken care of by our national health insurance) but it can be very handy.
I used it in Paris, where I didn't have a regular doc and had a flu.
In smaller cities, more so in villages or in the countryside, your regular doc can come and visit, as older people might have difficulties moving, or the practice might be far away.
I think in most western European countries this is normal, at least when I was kid (growing up in the Netherlands) it was. However, I haven't lived in Europe for the past 10 years so maybe the messed this system up as well.
In smaller cities, more so in villages or in the countryside, your regular doc can come and visit, as older people might have difficulties moving, or the practice might be far away.