the three-dimensional scrolling background!!!
When I first started playing Touhou, I barely even registered the backgrounds, and I think that's kind of the point... there's too much going on in the foreground anyway! But I started to look more closely at them and really appreciate them - especially after watching playthroughs the PC-98 games like Lotus Land Story, where the backgrounds are pixel art and clash more with the busy foreground.
I love these so much!! They're so surreal, some of them are totally ungrounded from reality, but they feel so cool to fly over. These backgrounds do a great job setting the location and tone of every new level, as they peacefully scroll by while to read the prose that appears alongside them. When enemies show up, they almost seem to fade away and never distract from the twelve thousand bullets onscreen, but every once in a while things calm down and you get a chance to appreciate that you're actually traveling through a living world.
And of course, they're used to awesome effect in some levels, like Perfect Cherry Blossom's stage 4 where you break through the clouds into the sky during the Lily White fight, and Imperishable Night's stage 4 when the central threat of the game, the moon, fades in and takes up half the screen... All of the enemies suddenly vanish, and you just sit and watch the forest break into this clear view of a giant, glowing moon, and only after a few slow moments does a boss character fly up to stop you. The timing of these transitions feels so well-crafted every playthrough.
Touhou's mainline games have so many good things going on with the characters and music and gorgeous bullet patterns, but damn, even all the less prominent design choices are still just so aesthetically unique and interesting!! I want to try experimenting with things like this in my own games...
(backgrounds courtesy of Touhou Memories)
One of my ongoing frustrations is that I used to own a really excellent book, The Invisible Art: The Legends Of Movie Matte Painting (2004), but lent it to someone and never got it back. Now, as more and more time passes with the book out of print, the cost of copies online has only gone up, with copies of the original hardcover selling used for over a thousand dollars. 
If your local library has a copy or something, I enthusiastically recommend checking it out. Great consideration of what goes into the wild balancing act between making art that is cinematic and evocative and making art that is unobtrusive and natural.
