Let's see here;
In Rainbow Six: Siege which I've been playing a lot lately, I usually tend to pick Ash or Blitz if I'm on the Attacker side and either Rook or Doc on the Defender side. Ash I pick due to her fast mobility, weapon selection she has, and her Breaching Rounds since they can allow you to open up a place from afar and they aren't electronic which would be worthless if you were going up against a Mute and possibly a Jager, mix that in with Breaching Charges and she can open up so much areas on the map. Blitz I choose due to him being a tank shield user, which I like using Shields if possible in these types of games since they can allow me to protect allies and I specifically like choosing Biltz as the Operator I use who has a shield since he uses a Flash Shield which can blind enemies. As for the defenders Rook and Doc, it all depends. Rook because he can give extra health to the entire team and give him a higher chance to go in the Down But Not Out status which always helps, and Doc since he can revive ally players from afar if they are down and for more health, and he can use it on himself. Not to mention they both use the same weapons, and it depends on who I feel like playing as or if someone picks the other since Rook and Doc are a beast combination.
In League of Legends, I'll usually choose Sona, Thresh, or Janna if I'm Support which I usually tend to play. I had invested the most out of these 3 in terms of Supports, and when I do play as Support, I perform at my best between all of 3 of them. It all depends on team composition mostly. If I'm ADC then I'll choose either Caitlyn, Miss Fortune, or Vayne for almost the exact same reason as the Supports I mostly choose, although it doesn't depend on Team Comp, but rather who I feel like playing as. Any other position, I don't care who I use since I got little to no experience as a Top Laner, Mid Laner, or Jungler.
In Team Fortress 2, I'll go for the Medic most of the time since I love playing as Support characters and I do my best as a Support character in pretty much almost any game that I do play and between the 3 Supports of TF2, I'll pick Medic as my go to character since I prefer his playstyle the most.
In Call of Juarez: Bound in Blood, I'll prefer to play as Ray McCall over Thomas McCall most of the time since he is the tank between the two and I like his special more than Thomas's.
In Borderlands, I'll choose Lilith and in Borderlands 2 I'll choose Zer0 since because of their special abilities to turn invisible and sneak up on enemies.
In Dead Island, I'll mostly choose Purna (if I remembered her name correctly) since she specializes in guns and gets a bonus to sharp weapons as well and I like to have that double bonus especially with the guns for later on in the game.
I can't remember anymore games at the moment and what characters I like to play as the most, but if I do remember some, I'll add them.