Spider-Man is often said to have no specific weakness, or at least none that is integral to the plot in the way of Superman's weakness to Kryptonite. According to his Marvel character profile, Spider-Man's precognitive spider-sense and superhuman physical abilities make him virtually impervious to harm.
However, Spider-Man's character profile also states that he can sabotage himself by cognitively overriding these autonomic reflexes. In other words, lacking faith in his own instincts would represent a serious weakness.
His dependence on his instincts might also be considered a weakness. For example, when a common cold weakened his spider-sense in "The Amazing Spider-Man #39" (1966), the Green Goblin gained a distinct advantage over him.
Like many superheroes, Spider-Man is also vulnerable to electricity, as well as family or personal ties, such as the ill health of his Aunt May.