Rolled up newspapers being hit with a (soft wooden) stick are meant to be good for body and face hits.
– Paul Arnold, Gordon Hall
Hitting real meat, use a baseball bat to hit leather jacket wrapped around baseball gloves, add breaking of chicken bones.
– Ben Burtt
A regular old bull whip crack is good for those over-the-top Street Fighter type punches.
– Don Diekneite
I’ve used the newspaper rolled up approach in the past and it’s hard to get a satisfying sound out of it. One of my favourites is wet mud, jump up and down, hit it with a bat, add some foliage for extra texture. Rotten fruit is always good for flesh squishes. The other day I was blending some carrots with a hand blender which created a wonderful consistency, simply pulling out the blender made some lovely squish noises.
– Paul Weir
If you need some great fight sounds to work from, this close combat effect library is worth checking out.