I would say Zelda, because that game RULED for 13 years, but it definitely lost its charm at Skyward Sword, and the new Dynasty Warriors version is a storyline-poor insult to the franchise. Almost as bad as Link's Crossbow Training.
I would say Elder Scrolls, because that game was THE BOMB, and it just kept getting better and better up until ESO, which made the series' overall quality drop down to 'Doom 3' level. (Not very good, for those of you who were about to spend the $40 in order to find out.)
I would say Doom, but Doom 3 lowered the series' overall quality to "Alone in the Dark" level. (The first one was the ONLY one worth playing.)
I would say Silent Hill, but it's had so many more downs than ups that I don't even know if it could be called mediocre anymore. (However, the fact that Guillermo del Toro and the guy who made that ghosty anime about spirals are working on the PS4 one is making me MUCHO HOPEFUL.)
There's Mario, but it's the same fucking game over and over again.
There's Earthbound, but the fandom never shuts up, and that ruined the game for me.
There's Metroid, but Other M , as well as the Deviantart Fan artkilled Samus permanently.
There's Fallout, but it leaves me wanting to play Skyrim after prolonged exposure.
There's Duke Nukem, but he's a misogynistic fuck whose jokes get less and less funny with every playthrough.
There's Wolfenstein, but the sheer mediocrity of the Xbox 360 reboot seriously detracted from the rest of the series, no matter how awesome it was
There's Monkey Island, but adventure games are kinda meh...
There's the Sims, but 3 is the only one worth playing.
There's Goldeneye, but GODDAMMIT ODDJOB!
Really, the only series that's consistently pleased me and didn't die horribly with age are the two Space Funeral games. Get them. Now.