It could be a classical piece or by a modern band.
Mine would have to be Crystal Ann by Annhilator:
I remember first trying to learn the lead part on this when I was about six months into classical guitar. Took me another six months, haha.
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I love a lot of instrumental pieces, but probably my favorite is the first movement of Vivaldi's Winter:
Other ones that are close to favorite are pieces by Satie, Debussy, Brahms, Mozart, Bach, Beethoven, Liszt, Chopin, Tchaikovsky, Saint-Saëns... and probably some composers I forgot about XD
In a non-classical way, Jazz Fusion is cool, like Marcus Miller and Herbie Hancock. Movie soundtrack composers like Hans Zimmer and Vangelis are great too. There's also some modern piano songs that are cool, like Yann Tiersen and Yiruma.1