One clear example is, League of Legends. Where you start with set of free champions and you either play or pay to unlock more of them. One can argue that, Valve's TF2 and Dota2 are in similar vein. You of course, don't have to pay to unlock heroes - but you pay to buy cosmetic items (so as you can look cool in-game). So, while you may dislike this model, it looks like it is here to stay.
The other issue is that it seems like often paying wouldn't be much fun either as it makes the game to easy.
More importantly I agree that this model heavily encourages the developer to design around that methodology (well described as "gamed" above).
To be fair, in this specific example - if I recall in Triple Town, the main thing you bought was unlimited play-time ("turns") for $3.99 (which follows the more positive unlock model). After that you could buy the standard coins (the shitty model), but given the design of the game I never understood why you would.
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.