There there is - TF2 and Dota2, F2P model. Where you pay to buy cosmetic items, but it does not affect game play one bit.
In those games, you can play without spending real money, but it's going to suck and not be as fun. These are the types of games that have the most backlash because they just seem so "greedy".
In games like League of Legends and Angry Birds, you don't need to spend money to get the real game experience. You can still play just fine as a free player and spending money seems more like a bonus instead of a necessity.
In contrast to arcade games like Mega Jump, Jetpack Joyride and others. Where you can do pretty well with a couple IAPs that will last throughout majority of your time playing.