I've been mulling this list for a few days now because it was really hard to pick. I finally chose the performances that had the most impact on me personally (so this list is going to be strange to most). Disclaimer: I didn't watch much during the 2010-2014 years. I was really more of a casual till the 2014 Olympics.
In chronological order:
1. Mirai Nagasu - Carmen Fantaisie - 2010 Olympics FS
There is just something about being 16 you're fearless and the future is bright. Skating last at your first Olympics, after Yuna, Mao, and Joannie, the loud cheers even before she took the ice... the smile, the pure joy she felt performing this program...these are things I really haven't seen from Mirai since. I always wonder what could have been. (I love her 2010 Worlds SP for the same reasons). Mirai holds a special place in my heart because I was living in Japan at the time teaching English. On the day of the 2010 Olympics, all of us teachers gathered in the teacher's room to watch - Mao vs. Yuna was the event of the century. Then Mirai comes on. Her name is in kanji next to the American Flag. Except for the Japanese and Chinese skaters, no one else had their names in kanji. My Japanese teachers were super confused. "She's Japanese...but she's American?!....no but she's Japanese..." They were even more confused when she was interviewed in Japanese later. And so I got a chance to explain to my teachers the difference between "ethnicity" and "nationality." The "yes she is ethnically Japanese but she was born in America, lives in America, so therefore she is American." Thanks Mirai for that moment!)
2. Jason Brown - Riverdance - 2014 Nationals FS
As I said, I was more of a casual figure skating fan...until I saw Jason's Riverdance. This performance really brought me back to figure skating. (Bonus: I have a friend whose knowledge of figure skating was basically "Yuri on Ice." I showed her this performance and now she's been to more live competitions than I have and we're going to Worlds together!

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3. Mao Asada - Piano Concerto No. 2 - 2014 Olympics FS
What a redemptive performance! After the heartbreak of the SP to come back and skate lights out. Such an easy-breezy 3A and the beautiful footwork sequence at the end.
4. ShibSibs - Fix You - 2016 Nationals FD
It was a toss-up between "Fix You" and "Paradise" but I think "Fix You" had a much bigger emotional impact for me, especially seeing their reaction in the kiss n' cry. And no one twizzles like the ShibSibs (and really, who else would throw in extra twizzles just for fun?)
Honorable mention: Mambo No. 5 (because it's just so fun!)
5. Ashley Wagner - Moulin Rouge - 2016 Worlds FS
This may have been Ashley's best performance ever. She was so completely into the program and lost in the moment. The cheers for every jump she landed and the roar of the hometown crowd before she entered her final spin was incredible.
6. Shoma Uno - Buenos Aires Hora Cero - 2016 GPF FS
I think this performance is what really made me take notice of Shoma. Sharp movements, passionate skating, love the 3A right on the music! I guess you can say I got "shoomed"! (This whole GPF was actually really poignant because to me it represented the "changing of the guard").
7. Nathan Chen - Le Corsaire - 2017 4CC SP
It was hard to choose a favorite Nathan program but I finally decided on this one. His reaction after falling out of the ending pose was just hilarious. This moment marked the beginning of (what I hope is) a long and beautiful rivalry. Although my favorite moment from this competition was actually the green room during Nathan's free skate. Patrick is saying to Yuzu "He's 17!" Yuzu himself is burning in kuyashii, and Shoma doesn't know what to do so he just copies Yuzu. XD
8. Yuzuru Hanyu - Hope and Legacy - 2017 Words FS
Again a toss-up between this and GPF 2015. Although the GPF performances were perfection, the 2017 Worlds performance was more emotional. Sitting in 5th place, to lay it all out there... "Never underestimate Mr. Hanyu!"
9. Tessa Virtue and Scott Moir - Moulin Rouge - 2018 Olympics FD
Ice dance has never been so sexy. After this my live stream kept freezing so I just determined that Tessa and Scott were so hot they must have broke my internet.
10. Weijing Sui and Con Han - Rain in Your Black Eyes - 2019 Worlds FS
I've only watched it 27521246 times.
10 is so hard! I had to leave a lot of my other favorite performances out.