They're not that old, but Yakuza.
Played 3, 4, and a tiny bit of Dead Souls back in 2013. Loved them (3 and 4, at least), and was excited about 5, but sort of passed it by.
Then October 2016 rolls around, and I decided to play 3 again, expecting to only play a couple hours, but I played through the entirety of it, then moved on to 4 again, and restarted (and actually finished) Dead Souls, then immediately bought Yakuza 5. It completely revitalized and amplified my love for the series. It was an extremely good week for me. Then a few months later, Yakuza 0 came out and is my GOTY 2017.
Now I can say with absolute certainty that Yakuza is my favorite series at the moment. Going back to replay games, even if they're not that old, can really change your perspective on them.