Not sure what you mean there. I include the fat in the simmering process, but skim it off the top after it cools. Still tastes great.
Wow. I make soup every week, but I’ve never done any of the good techniques listed here. I’ll try some soon!
At any rate, I just do basically what you described, but then I add one of these nice “stock pods” from Knorr:
http://www.knorr.com/product/detail/245812/chicken-stock
to bulk up the flavor and richness of the stock. It makes a HUGE difference–I add one of those suckers to almost every soup I make.
Also chiming in with the “add more salt” chorus. You can make a really tasty soup with not much more than salt, pepper, and a goodly dose of thyme for seasoning, although I usually add whatever else strikes my fancy from the spice cabinet.
Sunday is soup day at my house!
I disagree. Once the soup is finished and cooled, I skim off the excess fat. By that time, all the flavor has been drawn into the broth itself. The two biggest things that dull the flavor of chicken soup are insufficient salt and excess fat.
I did ask about spices but it came out species. 
And if you DO use breast meat (I use a mixture of breast and thigh), add it at the end so it doesn’t dry out.
Agree on the cracked fresh black pepper!
I also add some spices to the onions and carrots while I sautee them. It helps the spices open up. I learned that from Indian cooking.
Also – a couple of rotisserie chickens make excellent stock. I buy a rotisserie chicken, eat on it all week, then chop/disjoint/generally act like a cavewoman the carcass apart and freeze it. You can also freeze the tops and tails of most veggies (including the skins of onions, which can add a nice colour). When you have a few chicken carcasses, just dump them and the veggies in the stock pot and simmer as others have suggested.
I’m not a fan of potatoes in chicken soup because they suck up the salt. But I do like rice and will use wild rice. Lots of seasoning already in it, and the wild rice adds a nuttiness that’s yummy.
This has inspired me and I’ve got a pot going now. Sadly, I didn’t have any chicken carcasses, so I’m using Rachael Ray’s stock, which is surprisingly good.
Gotta disagree with the 2 dill recommendings above. I love dill but it doesn’t belong here. But yeah you missed garlic and seasoning at a minimum.
I was trying to remember what ingredient my *bubbe *used, when i was a kid, that made her chicken soup so special. Feet and unformed eggs. She used to get whole chickens, minus the heads and feathers. They always contained small egg yolks in various stages of maturity. The yolks went into the soup with the feet, which were quite tasty when removed.
And yes, dill. In fact, a handful of it, fresh.
must-haves:
1 chicken
1/2 celeriac
1 leek
1 onion
4-5 carrots
3-5 cloves
2 bay leaf
pepper
salt
water
optional:
some juniper berries
thyme
ginger
nutmeg
white wine
You might want to roast the chicken and onion in your pan first, then add the water to completely cover the chicken and throw in the other ingredients. Bring to the boil and then let it simmer for at least 2 hours. Separate broth from the rest (take care that you remove the cloves, bay leaf and juniper berries). Definitely reuse the cooked meat by picking it from the bone. Don’t reuse the squishy vegetables.