I like to 'break the system'. So I will usually make a character that uses unusual traits to maximize succes. That includes stuff like paying spells with blood and then healing upon hit in Path of Exile.
In Skyrim I used a conjuration/illusion mage. This ended up with me just summoning crap all day while no one could hurt me because of invisibility. Did get boring after a while though (no challenge).
I sometimes go assassin (Nightblade(illusion/onehanded)) which can be fun, but I will usually just end up coming out of the darkness and start attacking everything.
My favourite class is usually mage, because they get all kinds of cool stuff. I mean, swinging a sword is great and all, but shooting lightning is so much better.
In League of Legends my role is generally jungler, because I am good at keeping track of what is happening around the map. It is quite a thankless job though, since every little mistake everyone makes gets blamed on you. My favourite champion is Udyr, because of his insane snowball potential and dueling.
In making a character I tend to pay the least amount of attention to things like bribery and charisma. I prefer making my character more potent over giving him the ability to talk his way out of sticky situations.
For abilities I like things that buff my stats. So for instance, in Dark Souls I went with Sunlight Blade to enhance the damage my polearm did.
I find myself focussing all my stats on one 'core'. This way the playstyle revolves around a single thing, but the character will be extremely good at it.
I don't play MMOs or MMORPGs, so I can't speak for those.