Okay, perhaps not the most universal answer, but I felt that way about the show I've seen more times than any, Dirty Rotten Scoundrels. Sure, being a comedy, in terms of the material on its own, there may just be getting some of the more "mature" jokes or watching other nuances on stage. But for me, the cast was so amazing, they made every performance very different, so there was always something new to see, I never felt like I was watching a carbon copy for all of the times I've seen the show. Plus they made small changes every so often, and even the energy of the audience I found would affect my experience of the show. I guess we all can say this about shows we have seen over and over, though.
In a more...convential, what-the-thread-is-looking-for answer, I always got something new out of the Sweeney revival. I mean considering the first time all I really did was stare at Diana playing the clarinet...and the first 2-3 times I was so fascinated by the instruments, that it was a totally different experience when I finally paid more attention to the show. And when I started doing that, there was always more to see, to contemplate. Actors certainly changed and improved their performances, but to just look around what was going on the stage, to pay close attention to the lyrics, to the directions, little blockings that indicated character relationships, not to mention the analysis one could do of the score in its motifs and stuff.
Rent I think fits this too, though sometimes the cast takes away. Even with the movie, which I saw several times in the theatre, which never was different, I would notice something else that would effect me, kind of cling on to one character's journey each time, and each journey I found to be so rich that it opened my eyes to new things each time.
Hairspray is another I find that there's always something going on stage that yuo may not notice, but if you see it several times and look around, you'll find funny things going on that you didn't notice.
Spelling Bee obviously is different each time, with different speeches from Logan, and different audience participants.
Even Tarzan which is a guilty pleasure, I find little humorous moments that I haven't noticed with each time I go. Usually sitting in the front row probably helps me to notice these moments.
Les Miz I cling on to different parts and really examine them. If nothing else, the line "to love another person is to see the face of god" usually gets me crying, but at certain performances, a particular death will haunt me...last time I went I ended up in the third row, never so close, and when Alex sang about letting Cosette go, it just got to me seeing that performance and sadness up close, and that never affected me like that before.
Phantom, sitting in the front row for that show was a very different experience, truly amazing.
Mary Poppins I always get mesmerized by new effects I notice, or try to figure out how some effects are done.
If it's not obvious, I very much enjoy seeing many shows multiple times
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli