Hmm. Favorite character. Most of the games I loved growing up didn't have much in the way of characters. You either were some cardboard cut-out, or there was a story but you outfitted up your own Mage/Warrior/whatever and put your own specific personality and name there. It wasn't really until I got my PS2 and GBA that I started playing games with fleshed-out protagonists and parties.
I'm going to go with the guy in the icon -- Phoenix Wright. There are other characters and other stories that yanked at my heartstrings, but this one dragged me into a fandom and I'm still loving it three years later. Granted, I love lots of characters in the story, but the protagonist heads the list. He's an idealist, ridiculously loyal to his friends, snarky without being cruel (note: I still find this true in Apollo Justice, though not everyone does), intelligent, and well-rounded as a character despite the limitations of the game style.
It doesn't hurt that I love the text adventure / graphical adventure genre in general; the older games still didn't have protagonists so much as player characters, but like everything else, the genre has evolved.
And if there's anyone reading this who hasn't played the games, if you have an iPhone the first game is on there and is like $5. Try it.
Runners-up: Rosella, King's Quest 4 for having a story and being a female protagonist when that just wasn't done, and Yuna, Final Fantasy X for facing a destiny that sucked unflinchingly, and lots more I will kick myself for not including when I am more awake.
The rest of the days:
Day 1 - Very first video game.
Day 2 - Your favorite character.
Day 3 - A game that is underrated.
Day 4 - Your guilty pleasure game.
Day 5 - Game character you feel you are most like (or wish you were).
Day 6 - Most annoying character.
Day 7 - Favorite game couple.
Day 8 - Best soundtrack.
Day 9 - Saddest game scene.
Day 10 - Best gameplay.
Day 11 - Gaming system of choice.
Day 12 - A game everyone should play.
Day 13 - A game you’ve played more than five times.
Day 14 - Current (or most recent) gaming wallpaper.
Day 15 - Post a screenshot from the game you’re playing right now.
Day 16 - Game with the best cut scenes.
Day 17 - Favorite antagonist.
Day 18 - Favorite protagonist.
Day 19 - Picture of a game setting you wish you lived in.
Day 20 - Favorite genre.
Day 21 - Game with the best story.
Day 22 - A game sequel which disappointed you.
Day 23 - Game you think had the best graphics or art style.
Day 24 - Favorite classic game.
Day 25 - A game you plan on playing.
Day 26 - Best voice acting.
Day 27 - Most epic scene ever.
Day 28 - Favorite game developer.
Day 29 - A game you thought you wouldn’t like, but ended up loving.
Day 30 - Your favorite game of all time.