The scene where they both talk and he tells her everything that happened.
Very touching and very well acted.

The home movie scene is the one that touched me the most. The whole scene is moving. But especially when Hunter says "Goodnight, Dad" to Walt, then turns to Travis and says "Goodnight, Dad". It sounds corny describing it, and I'm not usually a person moved by easy syrupy bits. But I have to admit that one gets me every time. I'm getting a tear in my eye just sitting here writing about now!
A close second: a few moments after that, the conversation Hunter has with Anne as she puts him to bed. Hunter says about his real mother (paraphrasing) "That's not really her though. That's only her in the movie a long time ago in a galaxy far far away."
The "galaxy far far away" line is so natural, so much like something a real little boy would say. Hunter Carson must have said it spontaneously. No writer would think of that.

Bits, please, bits!
Many, many bits, I have to say. I was in tears half of the movie, mostly the later half, though.

Maybe not an obvious choice, but when Hunter is trying to explain relativity to Travis over the walkie talkie. It was such a brilliant glimpse into Hunter's fascination with the universe and his simultaneously clumsy and advanced understanding of some pretty complex principles. Beautifully acted and shot, too.

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The part where Travis encounters the screaming man and just ever so briefly touches him gets me every time .

"Also, Travis and Hunter "walking down the street" together."
you got it

Probably the scene where Travis is talking to Jane, in the phone booth. One of my favorite scenes ever, just amazing.
Also, Jane reuniting with Hunter while Travis leaves, and even the home-video scene.

Ending scene in booth.
When Jane reunites with Hunter.

Definitely the parts at the end with Kinski's character, especially
her reunion with Hunter.
It didn't move me to tears, but those were the most touching moments in the film.
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I thought the part where he recites his story to Jane in the strip club. That is a perfectly acted and directed sequence, you have him reciting the story with his back turned to her so he can't see her cry and just her face when she hears everything being told, Its a scene that was just well done in every single sense of the word.
This. In fact, like most people, the scene where Jane was reunited with Hunter also had me bawling like a baby. The first time I saw this film, I didn't truly think it was special until that final half an hour or so. The scene where Travis confronts Jane was a big part of that. It transformed my opinion of the film and everything else slot into place and became majestic.

Definitely that one, though the home movie is a close second.

I saw it. A thing that was cold and dry. It was me. - La Belle Noiseuse

I thought the part where he recites his story to Jane in the strip club. That is a perfectly acted and directed sequence, you have him reciting the story with his back turned to her so he can't see her cry and just her face when she hears everything being told, Its a scene that was just well done in every single sense of the word.
"I have always valued my lifelessness."

You must be a smart kid, I don't think too many 17 year old kids could appreciate this brilliant film.
There are so many tragic, touching moments in the film, its hard to choose. I really like the scene where Travis and Hunter are at an all-night laundy mat, after Travis has been on a drinking binge. Their conversation in this scene is amazing. Hunter is amazingly smart for his age.
Who's High Pitch?

The ending. Not when the mum and son meet but the final fade shot where the dad is staring up at the hotel. This film had tears in my eye the whole way and made me really sad. I'm a 17 year old boy as well. It just reminded me a lot of my own broken relationship with my parents

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This film is just perfect. So well made and acted, so emotionally draining yet uplifting. Something you experience and feel.
Thank you Wim Wenders. One of my favourites.
As for the bit that really gets to me: in the diner, when Walt is talking to Travis about Hunter Stanton's eyes say it all.

I thought the home videos thing was a bit cliche. it just seems like the go-to technique to invoke pathos. maybe it wasn't as cliche in the 80s but it still didn't move me.
the most touching was probably when he starts to recite his story to Jane in the strip club, though it goes on slightly too long for my liking.

I have to second the end when Jane is reunited with Hunter. I NEVER cry during movies. NEVER. I don't shed tears on a regular basis to begin with, only under extreme situations (usually involving death of a loved one or the like). When she walks into the hotel room and he turns around and sees her and the two hug, I was almost bawling. I've never had that happen, so this movie is kind of monumental to me.

Two bits:
When Jane talks to Travis about how much she missed him after he left.
When Jane reunites with Hunter.
The dust has come to stay. You may stay or pass on through or whatever.