1. Mishkutenok/Dmitriev LP 2001 worlds
2. Sui/Han LP 2019 worlds
3. Sui/Han SP Blues for Klook 2017 Worlds
4. Sui/Han SP Spanish Romance 2016 worlds
5. Sale/Pelletier LP Olympics 2002
6. Sale/Pelletier SP Olympics 2002
7. Duhamel/Radford LP 2016 worlds
8. Underhill/Martini 1984 LP Worlds
9. Kazakova/Dmitriev 1998 SP Olympics (I know people thought the music choice was weird, but I thought it was out of the box and I liked it.)
10. Peng/Jin 2019 SP worlds
The first is, I think, maybe the best pairs program of all time from the great Tamara Moskvina.
Surprisingly, nobody has mentioned them yet, but you should view some Gordeeva and Grinkov programs. They weren't my faves, so I didn't include them in my previous list, but they are iconic pairs skaters. I preferred their programs as professionals, if you are looking for a place to start. Many revere their second Olympic gold medal winning Moonlight Sonata program, as well.
Whew - anything that Gordeev and Grinkov did. Anything. The statement "skating as one" really applied to them.
I also think Denis Petrov was one of the best male pairs skaters and his ability often is overlooked. I remember seeing him skate a pairs program with Kristi Yamaguchi in a Stars on Ice production and wishing they had competed together - it was that good.
I loved Mishkuteniok/Dmitriev in 1994 LP (where they got a silver at the Olympics) and I adore Savchenko/Massot's La Terre vieu du Ciel (the gold at both Olympics and Worlds in 2018) FS and Lighthouse.
Gordeeva / Grinkov, Moonlight Sonata Europeans FS,
Yamaguchi / Galindo, Romeo and Juliet,
Berezhnaya / Sikharulidze, Swan Lake SP,
Pang / Tong, Olympics FS in Vancouver,
Savchenko / Massot, anything including Art on Ice and FaOI.