1.) The Legend of Zelda
2.) Kingdom Hearts
3.) Pokemon
4.) Resident Evil
5.) Donkey Kong

There are other games that could have made this list provided that they are not categorised under:
Series fatigue - Assassin's Creed
Dormant series - Prince of Persia, Golden Sun
Series quality decline - Final Fantasy (this one appears to have the most potential to redeem itself), Fable

That seems to be the gist of it.

Yeah. Golden Sun would be in my top 5 and replace Zelda if it was a series that was continually made.

I am only going to choose franchises where there are multiple games in the series that I love, so I can't include Valkyria Chronicles and Dark Cloud, because I only love one game from each of those franchises.

1) Persona
2) Starcraft
3) Pokémon
4) Final Fantasy
5) Ratchet and Clank

1. Legend of Zelda
2. Mario
3. Resident Evil
4. Metroid
5. Pokémon

1. Mega Man
2. Mario
3. Souls series
4. Fallout
5. Ghosts`n Goblins

Pokemon
Monster Hunter
Megaman Battle Network
Mario Kart
Naruto Ultimate Ninja Storm

Latest Pokemon games are becoming a bit less interesting and disappointing but it still remains #1.....for now.
Honorable mentions-
Gears of War
Darksiders
The Wolf Among US( Yes season 2 was confirmed)

1. Final Fantasy
2. Metal Gear Solid
3. The Legend of Zelda
4. Kingdom Hearts
5. Pokemon... Persona is coming for you though. Better Step up your game for Gen 7.

Might & Magic
Super Mario
Fallout
Uncharted
Diablo

1. Pokemon
2. Zelda
3. Metroid
4. Mario
5. After that they kind of just blend together.

1. Final Fantasy
2. Star Wars
3. Elder Scrolls
4. Pokemon
5. Batman: Arkham