Mega Man - My favorite series of all time. I've played MM2 primarily since I was young, but could never beat it as I kept getting stuck at the dragon boss in the first fortress stage. One day, I was determined to finish it and I did, setting me down a path to complete all the games I could. I love all the subseries, but Classic and X are by far my favorites. MM9 and MMX4 are my favorites here.
Mario - As a kid the first game I remember playing vividly was the SMB3 GBA version, but then I was obsessed with Nintendo and Mario as a whole and began seeking out every possible title in the series at that time. To this date I've played and completed every mainline title even up to the recent Bowser's Fury addon to 3DW. Personal favorites in the series are Mario 3, World, Sunshine, Odyssey, and M&L Superstar Saga.
Early LEGO games - Mainly Lego Star Wars 1/2/TCS, Lego Indiana Jones, and Lego Batman. The formula did get old after a bit but I still consider these memorable classics for me.
Tony Hawk series - Never was a sports guy at all but these games captured my attention all the time and still do. Especially THUG 1 and 2 and American Wasteland.
There's a bunch of others like Metal Gear that I really enjoy but I haven't finished all the main entries yet. I also had a Sonic phase when I was younger that I grew out of.