Sorry if I have posted any of these links before. I well may have. I am of course biased towards solo piano classical, since that's the instrument I play. And I definitely tend towards the Romantic Era. Definitely!
This is one of my favorites to play on piano. It took me a couple of months to get it to a "performance ready" state. It sounds deceptively simple. it is not.
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This one I like playing too (although it's been many years since I did - I need to go back and practice it!) I love the simple melody, and it's fun because you play just about all of that melody with one finger - the fifth finger of your right hand. Other fingers just kind of noodle around (you have to be relaxed to not tire those fingers, or it really ruins the piece).
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I also love playing this Chopin nocturne. Chopin is probably my favorite to play, although some of them can get so sweet that you have to take a break and play something else so you don't get cavities.
https://www.youtube.com/watch?v=ZtIW2r1EalM
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This Brahm's piece is delightful to play, although not quite as good to listen to. It is a very "thick" piece, with many complex harmonies. What makes it so fun to play are the vibrations of the piano from these harmonies. The audience can't feel that, but the pianist can. I would get goosebumps while playing many passages in the piece.
https://www.youtube.com/watch?v=20Gb0JcviRA
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This is one that I was never able to get up to the speed I wanted. The ending is so exciting and you end up half standing with the piano bouncing around when playing it. Many performers almost leap off the bench as the piece ends. Many people have heard this played on classical guitar, but the piece was originally written for piano. Everyone thinks it's Spanish, but the composer was actually Cuban. The piece is more interesting when you know the story it is telling. It is about a gaucho (cowboy) trying to win the affections of a dancer. He is singing his heart out to impress her, and she is dancing to impress him. You can easily pick out the heartfelt singing parts and the dancing parts. At the end, they become a couple. Not strictly a "classical" piece of music. However, the definition of a classical piece is not based on when it was composed. It is based on the elements and style of the piece. e.g., Rachmaninoff is considered classical, and he didn't die until 1943.
https://www.youtube.com/watch?v=3LGkE2lSKoA
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My favorite performance of Ave Maria. I could not play this. Few things with the name "Liszt" attached to them I can do ("Standchen" above being one of those few!)
https://www.youtube.com/watch?v=RCucnn-95nY
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This one is beyond my ability, but I love the piece. One, because it is beautiful. Two, because of the technical difficulty in playing it. It was written by Liszt - (which is why it's so stinking difficult!) He was quite the showoff in performances. He always found ways to get your hands into position to play a certain note at just the last second, often jumping over or diving under the other hand. Not easy to do at all. This is not my favorite performance of the piece, but it does a good job of showing what is required to play it.
https://www.youtube.com/watch?v=po_a1SmZKLs