The Therapist Gamer

This is a three-match game that is free on the Vita.  It takes a more thoughtful approach to the genre, kind of like Candy Crush.  However, the twist is that matching different colored pieces has a different effect in the overall gameplay.  At the top left of the screen are your soldiers who need to deal damage to enemies before the enemies take their turn to deal damage.  Red gems activate the swordsman, who does lots of damage to one enemy; yellow gems activate the rifleman, who deals moderate damage to every enemy on the front row; orange gems activate the bomber, who does moderate damage to all enemies, and blue gems activate the healer, who heals your soldiers.  You upgrade the effectiveness of your soldiers with diamonds, which you get from green gems.  If you collect enough cake from the purple gems then you can thwomp all of the enemies with the Fat Princess herself.  There are a variety of enemies who also get stronger as the game progresses, and there are even boss characters that can only be killed in specific ways.

 

There are a ton of "match 3" type games out there, especially on phones, but this one is a cut above the rest.  It has a layer of strategy that goes beyond that of any other "match 3" game I've played.  The main downside is that it is designed to have you spend real money on diamonds, so if you want to upgrade your soldiers without paying real money then you have to play for a bit longer than you would in a normal game.