I can't rank my favourite games by numbers because I really don't like to go with the "best game ever" term. Here are my top ten, of some franchises I may name several installments.
The Legend of Zelda - Twilight Princess, Majora's Mask, Wind Waker, A link to the past, the original
Metroid - Metroid Fusion, Metroid Prime 2, Metroid Zero Mission, Super Metroid
F-Zero - F-Zero X, the original
Mario Kart - Double Dash!!, DS, Super Mario Kart
Super Mario - New Super Mario Bros, Sunshine, 64, World, Bros 1 and 3
Paper Mario - The thousand year door
Fire Emblem - 7 and 9 (haven't played 1-6)
Baten Kaitos - Eternal wings and the lost ocean, Origins
Final Fantasy - 7, 9 and X-2
Resident Evil - Remake, Zero, 4
It's really hard to make a top 10 even with naming several games of a series, there are so many more great games like Soul Calibur 2, Contra 3, Ikaruga, Tales of Symphonia, Sonic Rush, Banjo-Kazooie, Breath of Fire 5, Project Gotham Racing 2, Colin McRae Rally 2005 and some older games I can't think of at the moment.