IU totally agree since I play League of Legends but I'm not really good at it. You can spend money if you want but it wouldn't make you stronger than other players that's why I like this game. A lot of games nowadays would require you to pay money just to be strong in the game.
My hubby plays MMORPG games like LOL and DOTA and I believe you can play it without paying a single dime. There are also other choices like Arcade games which you can play online for free, but most of the good ones does not come for free, you have to pay for them. Some developers will let you play their game for a certain span of time and let you decide after whether you would like to purchase the game and continue playing it or not.
Criminal case is 100 percent free but you needed to have a lot of facebook friends to make the game enjoyable to play. This one is not really an online game, Legionwood is an offline game that plays like the old Final Fantasy Games. It is a vert enjoyable JRPG and it is 100 percent free.