Punch and impact effects are hardly ever knocked up on a computer. Listening to the high-middy classic punches from classic games, they probably snapped a stick, or whipped a big pillow with it, then pitched the sound down a few semitones, brought out the punchy mid to low frequencies, then layered some milder low frequency sounds on top.
But for most punch sound effects, they actually record something hitting a lump of meat or something similar. These days, even a real person will be punched to get a genuine sound.
As for attempting to design this type of sound, I would look into creating it the same way you would create a kick drum hit, but higher frequency and wetter with a fast decay. Try layering it with a low frequency clap type sound, or some band pass filtered noise with a distortion effect. Add reverb depending on the environment, but keep it tight. I think the key for this design is layering.
This article on punch sound effects looks like a good read for you, although I've only skimmed it.
Read the 'Punch Sounds' section of this article on EpicSounds.com; It seems more old school, like the classic effects used on Super Mario games. There's also a 'Body and face hits' section(sections listed alphabetically).
This previous question from 2011 is similar to yours and has a few answers.