Take a look at this list of games that play like Puzzle and Dragons. Developed by GungHo Entertainment, PAD is a puzzle RPG available to all users on iOS and Android and has been localized for various languages as well; find the one that fits you! These recommendations are based on the match-three mechanic exclusively, with an emphasis also on detailed art design and ease of play. If you're an extreme fan of the match-three mechanic, RPG flare, and cool graphics (or any combination of the three), then these should be right up your alley.
Games Similar to Puzzle and Dragons
Candy Crush Saga can get extremely stressful, and have you spending a little more than you'd like if you're not careful. Therefore, take your time with this one and see if you can make it through all 100+ levels without needing a boost. Really though, if you haven't had any experience with this game, you should. King is one of the biggest developers out there, and their Saga games will keep you going for hours and hours and hours.