Even buying champions in LoL (you can buy skins too) doesn't affect the game really because every week the champions you get to play for free rotate, giving everyone a chance to play whichever they like and secondly, they are balanced so that it doesn't really matter which champions you play if you're skilled. You are really paying for a different experience.
So, the three models of free to play that I see are:
1. pay for perks - this is the traditional "you pay and you get something you can use", be it guns or coins or whatever. The danger with this model is that it is a very fine balance to prevent this from becoming pay to win.
2. pay for cosmetics - DotA 2 or skins in LoL or hats in TF2 or whatever you have. Buy things to change the look of your stuff in game, but buying things has no effect on your success or the gameplay. IMHO almost all free to play games should support this in some way.
3. pay for experience. The things you buy in game don't give you an advantage in the game but instead alter the play style or how you experience the gameplay. League of Legends gives you weekly tasters of the different gameplay experiences the different champions have to offer and you can pay to keep the ones you like best. I believe that this is the model (coupled with #2) that ultimately makes the very successful free to play games stand out from the merely moderately successful ones.