It may sound cliché, but using your middle initial in intellectual settings can actually increase others' perceptions of your intelligence, according to a recent study.
In a collection of seven experiments on the subject, psychologists Wijnand A. P. Van Tilburg and Eric R. Igou found that using middle initials increased participants' evaluations of writing performance and status—but only when used in settings related to intellectual performance.1
For example: in one study, 85 participants read a passage about Einstein's theory of relativity. Some participants were given a passage with the author "David Clark," while other passages were credited to "David F. Clark," "David F. P. Clark," and "David F. P. R. Clark." Passages that included the middle initial(s) were rated as higher quality writing than the passage without.
Again, this only really works in intellectual settings, so I wouldn't go around introducing yourself at parties as "John F. P. Merryweather." But if you're writing a book or beefing up your résumé, it might be worth including.