I'm sorry if this has been asked before. I'll start with mine
Oh it definitely has, multiple times... but it's fun to discuss it again every once in a while.
Top 10, however, that's pretty hard. I'd have a somewhat solid top 5, but I feel like I'm really gonna be stretching it to get to 10 entries here.
10. Tekken (...I guess. I do like these games a lot and have had plenty of good times with them anyway.)
9. Rock Band (and Guitar Hero. I don't play these much anymore, but they were a big part of my life and are still pretty fun.)
8. Super Smash Bros. (eh, I'm not a big fan of the first 3 games, but Smash is Smash.)
7. Portal (only two games, but I love them both.)
6. Pokémon (used to be much higher, but after recent games and ideas I'm a bit distraught.)
5. Splatoon (still plenty of unfulfilled potential on this one, but I love both games and its future looks very promising.)
4. Star Fox (a universe and characters I'm quite fond of. It could be a lot higher had it ever come close to fulfilling its potential.)
3. Ori (...I guess it counts as a franchise with an upcoming game next year? I'd hope so)
2. Metroid (I got started with in 2014, my love for it has only grown over the years.)
1. The Legend of Zelda (obviously.)
Edit: and for some honorable mentions I guess Mario, Crash Bandicoot, DKC, Sonic and the likes.