Chicken dishes vary hugely in style depending on how they are cooked, but you cannot really go wrong with a simple Chardonnay - not too overpowering for the delicate flavour.
Roast Chicken, Barbecued Chicken, Chicken Fricassée:
Unoaked or lightly oaked, fragrant Whites go best with everyday Chicken dishes and a simple Chardonnay is a safe bet with most.
For Roast Chicken with all the trimmings a mature Red Bordeaux is an alternative.
Chablis or White Rioja
Because Chicken Kiev is quite a greasy dish it will need a wine with noticeable acidity, so select wines from cooler climates. Chablis would be an excellent choice or to compete with all that garlic a White Rioja would also be good.
New World Chardonnay
Chicken Pie is quite likely to contain a creamy sauce which will need acidity but also cope with richer wines like warm climate Chardonnays such as those from Australia or North America.
Chicken Chasseur, Chicken Casseroles/Stews:
Tuscany Reds (Chianti, Rosso di Montalcino)
Reds or Whites from Vin du Pays or Languedoc
High-acid wines are needed if tomatoes feature heavily in the sauce and an Italian Red is probably the most tomato-friendly wine. To match the gameyness of the mushrooms in Chicken Chasseur choose a light-bodied Merlot.
Red Burgundy, Beaujolais Cru, New Zealand Pinot Noir
The rule for Coq-au-Vin is cook with the best wine you can afford and then drink the same, and this would be a Red Burgundy traditionally.
Alternatively a chunkier Beaujolais or New World Pinot Noirs such as those from New Zealand and Australia should also work well.