This is a purely speculative post. I don't have the answers, but I have questions. 
I was talking with a friend. He said he believed all music that was worth listening to was already created. I kind of agreed. We have classical music, rock, punk, grunge, heavy metal, electronic, instrumental and even awful music like dubstep.
I think the era is gone when a piece of music could influence a generation and stand the test of time.
In short: I don't expect to hear anything new that hasn't been done before. But there is a wealth of music already produced so maybe it's not a big deal.
I am going to list a few other areas that I think have peaked and my thoughts:
Desktop software: I think this is it. The desktop paradigm is not as strong as 10 years ago. “Progress” is happening in the mobile/cloud space. I don't think we will see new desktop applications we haven't seen before.
Skins/theming: There is an abundance of high quality, inspirational skins already produced. Actually I am amazed that the skinners here at Wincustomize continue to produce high quality skins/styles.
However I have a hard time imagining a totally new skin/style that hasn't been done before. Same goes for wallpapers. There are already millions of high quality wallpapers covering a wide spectrum of personal preferences.
Home electronics: We already have huge hi-resolution TV-sets, projectors and multi-channel sound. 3D for those that like that sort of thing. There are smart homes for those that wish to control their home like it's just another device. Now it's about incremental improvements. The big jump was from tube-TVs to flatscreens.
Areas where cultural progress seem possible:
Games: I think there will be progress in gaming/games. There are many more factors to play with. There is a technological factor that drives innovation. There are sound, visual elements and movement.
Artificial Intelligence: This is something that is just starting to take off. A lot of human interaction will be with AI in the future. Good or bad? Probably both.
Virtual Reality: This might become big when tech is ready. But do we want it?
Movies: Hollywood will continue to produce movies until the end of time. Some of them will be worth watching.
Summary: I think human “cultural” progress will largely be tech-based (including useful things like 3D printers and self-driving cars). The “fine arts” are dying (things created just to be beautiful). There will always be artists, but how do you create something outstanding that hasn't been done before?
Simple examples: I don't expect to see a new car that is more beautiful than a car that has already been created. I don't expect to hear music “that I haven't heard before”. I don't expect to see a new skin/theme that is “a new look”.
Everything has already been created... if not, where do you see room for improvement?
