I always liked the stories where Peter uses his intellect, rather than just his powers, to solve problems.

Some good examples are his first couple of battles with the Lizard. In the first one, he whips up an antidote to the serum that has transformed Curt Connors into the Lizard. You've got to be pretty brainy to do that. In their second battle, he lures the Lizard into a refrigerated train car, knowing that reptiles are cold-blooded and, thus, don't handle cold weather well.

Another good "Spider-Man outthinks the bad guy" story is his battle with Morlun in the JMS/JR Jr. era. I've been critical of the JMS run on Spider-Man, but this actually is a really good story and Peter beats a seemingly unbeatable foe by using his scientific acumen.