There's some post-Pvt Ryan stuff out there that you might want to reconsider. You've Got Mail was a fun, light and frothy rom-com and Hanks had great chemistry with Meg Ryan. The Green Mile is one of the best movie adaptations of a Stephen King book and Hanks is excellent in it. Road To Perdition is an excellent movie and I love it because Hanks plays against type - a disciplined killer who shows that there is honor even among thieves. Captain Phillips where he plays the captain of an unarmed cargo ship taken over by Somali pirates. There may be others too but these are the ones I remember off the top of my head.
I am from the school that thinks an actor is only as good as those around him. What makes Hanks so good is that, even with NO ONE around him, as in Castaway, he can turn in such a stellar performance. Further, his ability to be believable across multiple genres is something few leading men can manage with such aplomb.