My mother and mother-in-law used to make fantastic chicken soup fairly often, especially if someone was sick.
Their recipes were much like detroitdad's in their simplicity, except my mil would add a load of fresh, chopped parsley towards the end of cooking.
Also, the key to making a good soup was use a whole, skinless chicken, and to continually skim any foam/scum that floated to the surface when the chicken was initially boiled in broth. When the foam stopped forming, the heat was reduced and the diced veggies added (onions, celery, carrots). After about an hour, the chicken was removed, the bones picked out, and the meat was chopped and put back in the pot to continue simmering a bit longer.
A kind of strange thing my mil did was to add parboiled, cubed potatoes near the end of cooking to finish in the soup, then she would serve the soup over wide egg noodles.
It's a double hit of starch, but it's really filling, which I guess is good for someone who doesn't feel well enough to eat much.