Re: Spiderman vs...
From what I've been told, Spider-Man took on the X-Men in Secret Wars and since he does have a highly effective in combat danger sense and probably the most agile hero in the Marvel U, he schooled them....until Xavier pulled a mind whamy on him.
Also he did take on the Avengers in one of the early issues of the Marvel Knights Spider-Man (there was a misunderstanding when he broke into the mansion) and was really holding his own until Quicksilver showed up.
As for the FF, the only thing I can think of is waaaay back in Amazing Spider-Man #1. IIRC, he broke into the Baxter Building and got into a fight with them simply so he could show him what he could do in hopes of getting hired by them. If anyone knows if this is what happened or not let me know, I wouldn't mind expanding my knowledge of the character.