For me, the vote for favorite series ever has to be Fallout.
I've always loved post-apocalyptic settings (think Mad Max), so when I first saw Fallout 3 I knew I was gonna be interested in that game. Playing in the wastelands of society 200 years after nuclear war, what's not to love? I got Fallout 3 the day it came out, and sunk many, many hours into it. Because of how much I loved that game, in addition to reading various bits of lore in the game that refer to things happening before the events of the game, I did my research and later got my hands on Fallout 1 and Fallout 2, and loved those games honestly more than Fallout 3. I played those games to death, and had a different experience with all of them each time, siding with different people and factions each time. Of course I got Fallout New Vegas at launch as well and vastly preferred it to Fallout 3. Top notch writing in that game from a lot of the same people that wrote for the first two Fallout games. I loved how the games were role-playing games first with some shooter elements mixed in there. Then comes Fallout 4, a complete dumbing down of the series, stripping most of the RPG elements out and leaving us with a shooter that has some RPG elements tacked on so it'll "feel like Fallout". That's not to say I didn't put a lot of hours into Fallout 4, seeing as I'm going back and doing the DLC on my first ever character, but it still wasn't the same.
I can talk about Fallout for hours and hours, I know more than one person probably should about the Fallout series as a whole and lore of all the games. It's safe to say the only game that ever comes close to matching or exceeding the hours I've spend playing Fallout games is probably World of Warcraft. Ended up playing that game for about 9 years or so, the only time I ever unsubscribed was to play the Star Wars MMO that came out, get disappointed with it in about 2 months, and then immediately resubbed to WoW.
Some runner ups would probably be Final Fantasy series, which I've also spent an insane amount of hours playing. I have played every numbered one except for XII and XIV (the MMOs), XII I didn't play because I was subbed to WoW at the time, and XIV I don't currently play due to just being so burned out on MMOs in general. I also have yet to play XV, I heard there was some free story stuff coming out for it so I'm probably gonna wait for that to happen. I've played a ton of Disgaea games, Shin Megami Tensei/Persona games, pretty much every Rockstar game out there. The Dark Souls series are another one for me, I started with Demon's Souls back on PS3 and have played every single one and loved them to death.
For a standalone game experience, as in a game that is not part of a series or received a sequel, my hands down favorite is Vampire The Masquerade: Bloodlines. It's based on a tabletop RPG that came out in I believe 1991, and is a great experience anyone who considers themselves to be a RPG fan needs to play.
Basically this topic taught me that whenever gaming is brought up, I'm going to type a novel. Gaming is my favorite hobby and a huge passion of mine, what can I say?