As an actor who's never shied away from admitting that he got lucky in his phenomenal career -- and who's generally considered one of the nicest fellows in show business -- Tom Hanks has still managed to pull down an impressive roster of film roles. As to what the best of those roles would be ... that's bound to be highly debatable, and I'm sure the comments following this post will bear that out.
If one wants to go by Oscar-winning performances, Hanks won back-to-back awards in 1993 and 1994 for Philadelphia and Forrest Gump. But it can be argued that the first, while a fine performance, was lauded mainly for the "bravery" of playing a gay man, and for the important subject matter. In Gump, it was a measure of the (inexplicable, to someone who dislikes Gump intensely) popularity of that film, and for the Academy's affection for actors who play characters with physical or mental disability.
His savvy for choosing excellent dramatic roles in films like Road to Perdition, The Green Mile and Catch Me If You Can make his sincere work in the big, dumb Dan Brown adaptations palatable, but to really find his "best role," we need to go back to 1990, when Hanks was still considered a comic actor. After a string of hits and semi-hits that included Splash, Bachelor Party, Volunteers, Big and (ahem) Turner & Hooch, Hanks made a still-underappreciated gem of a film called Joe Versus the Volcano.