Upgrade to an Iron Skinning Knife as soon as possible. It will reduce your skinning time by 50% or more. This is very helpful when hunting Wolves since they can have a fast respawn time.
Skinning animal kills will usually yield both Hides and Raw Meat.
In a general order of fewest to most drops:
Elk: Doe and Stag
Farm animals (Pigs, sheep, cows)
Note: Alligators do not drop Hide.
Turkeys drop Feather, Poultry, and Eggs although not all three all the time. They are also the kill target for many Town quests and some Faction quests. When your Skinning and Tracking skill is high enough, they will show up on your compass.