Depends on my mood, because sometimes I do and sometimes I don't for scenes that I've seen multiple times, and it's not related to how many times I've seen it.

Sasuke's psudo-death was just well animated and acted.

Haku's death + Naruto's speech + Zabuza's tears + Zabuza going mad zombie with a kunai in his mouth + Zabuza's death = tear jerker.

Lee struggling with one-armed pushups after his massive injury.

I'm not one who gets teary eyed at every single "tear jerker" moment. But when it's characters that I've come to care about on that imaginary entertainment level, and when it's well acted (and well animated for animated things), yeah sometimes it gets me. Naruto is one of those great series that goes for the full impact of everything it dishes out from the "holy crap, that was kick-ass," moments to the instances of "have to wipe my eyes so I can read the damn subtitles." Interestingly enough (though not suprisingly), this rarely happens with dubs. I think the only time it did was towards the end of the Fatal Fury movie, as cheesey as the girl's acting was, Terry's reaction was right on the mark. And a few American movies have managed to do this (Ladyhawke and The Mighty are the only ones that come to mind).