I've tried brining a chicken (brine = 1 cup salt to 16 cups water, over 10 hours) and couldn't taste a difference.
Assuming you don't normally buy pre-brined / injected birds, you should notice a difference... As roux notes, it should be noticeably moist and tender, especially the white meat.
A couple of things to try:
- Increase the time in the brine. 10 hours is plenty for breasts or quarters, but a whole chicken may take longer. A whole turkey will definitely take longer!
- Check your salt. A cup of small-crystal table salt per gallon of water should be fine, but if you're using flakes (kosher and some sea salt), you may be producing too weak a brine! If in doubt, weight it out.
I've tried brining turkey, and wasn't satisfied with the results. The main problem is that the skin comes out too salty, no matter how well I rinse the bird. Another major issue is that the gravy comes out pretty close to inedible. Thirdly, you can't stuff a brined turkey.
So I've developed the following technique which gives me a moist breast, almost as good as a brined breast, but also allows for the traditional brown skin and succulent gravy.
The secret ingredient is ONIONS.
Slice several onions and line the bottom of the pan with them. The idea is that the onions don't allow any of the skin to touch the metal of the pan, so that skin won't stick.
Also add about two or three tablespoons of water/wine/stock/ just to cover the bottom of the pan to prevent sticking until the juices start flowing.
Stuff the bird if you are going to (Use a hot stuffing, it will help the bird cook faster, and you have less worries about undercooked stuffing). Otherwise, just stuff a couple of onions and celery stalks in. (Or stuff with mirepoix)
Assume a 3 hour cooking time, roast BREAST DOWN for 2 - 2 1/2 hours. Basting as needed.
When the bird is about 120 degrees (Still needs about 40-45 degrees more). Flip it over carefully, clean off any onions stuck to the skin, and bring the oven temperature up to 450. Leave it about 20 minutes, until skin is brown and crispy, and take it out at about 140 degrees. (if it's getting too warm, turn on the broiler to speed up crisping.)
Let stand out of any draughts for at least 20 minutes until the carry over takes it to 165 degrees.
Turkey has a huge thermal mass, and will continue cooking for at least 20 minutes.
This is also probably just the right amount of time to do the rest of the meal.
Cooking the bird upside down will result in a moist, succulent breast, without the oversalted skin and gravy that brining produces.
If you want to get the flavor of brining without all the work of trying it, you can buy kosher turkey. Part of the preparation for kosher meat is to pack it in kashering salt (where the term "kosher salt" comes from) to draw out all the blood. This means that the meat is essentially already brined. The most common brand in the U.S. is Empire, and they have both fresh and frozen meat.