I'd say the megaman battle network series.
It's a funny story how I got into them in the first place. I was probably around 12, I had recently acquired megaman 64 and it was one of my favorite games. I played it to death, looking through every nook and cranny trying to find everything. So the holidays came along and I wanted a new gba game, saw mmbn2 behind the glass at the local walmart. I knew straight away that's what I wanted.
Christmas came, I was stoked to open up my gifts including mmbn2. I was really impressed by it because at the time I didn't really own many games and the gba was my first handheld. I played it for a bit, quickly realizing that the only thing megaman 64 and megaman bbn share are the title. I thought the game was hard, go into the first boss level and never made it through. I didn't pick up the game for a while after that.
A few months later, I popped the game into my gba slot and started playing for a bit, I made it to the first boss and beat him. Then, a plot point dropped, and I played the game like hell all day and I remember making my way up to shadowman. I started getting better at the game and though frustrating the puzzles kept me entertained.
From that point on, I never looked back, I own them all 1 to 6. The story, the gameplay, the characters, it's just a really good series, I even love the shittier installments like 4 and 5.
Oh and of course, my favorite in the series will forever be battle network 2.
Jack in megaman, power up!