Spider-Man is the ultimate example. Some other good examples are as someone said Superman until he got trained by Mongul and then later by Wildcat. Luke Cage I don't think was ever trained by anyone in stark contrast to the disciplined Iron Fist. Blue Beetle (Jamie) and Booster Gold never were trained to my knowledge unless you count playing football as training for Booster before he got his gear.
Well I guess you could start with say a guy like tombstone? I don't think he officially has any training... But kingpin I think does...
Hawkeye was just a circus act prior avengers...
Bullseye I don't think... But I'm not sure...
Even the thing had some boxing lessons iirc... Pre cosmic mutation...
Although reed Richards probably has none
Max gargan I think was just a nut in a suit
joker, penguin, twoface, I'm not sure had training..
Bane I think did...