alt Hacker NewsDexter had the best internal dialog I can remember; it's like the protagonist had two greatly contrasting personalities (his outward demeanor and then his internal dialog) which were constantly riffing off each other on screen, though it never got in the way. Just pitch perfect throughout.
For a show where the internal dialog eventually does become a bit annoying, look at You (in my mind, greatly inspired by Dexter).
Dexter might have been the last one I watched that featured it heavily for sure. At least among live action I guess I should caveat, anime still uses it quite a bit as a shortcut.