Well, first and foremost, there's
Minecraft Pocket Edition, which never goes on sale, so it can be picked up any time without worrying about price drops.
PC/Console port/remake-wise, there's the
Grand Theft Auto series (III, Vice City, San Andreas, Chinatown Wars); Final Fantasy (III-VI, though it's important to note that Square Enix doesn't keep the updates on Amazon in sync with the Play Store, meaning it took months before Amazon users got versions that worked with Android 5.0 and gamepad support);
Sonic 2 is a good remake with plenty of bonuses;
Ticket To Ride is a good port that supports Cross-Buy with its DLC, as long as it's linked to your Days of Wonder account;
Gemini Rue is a point-and-click adventure that should theoretically work well on the touchscreen (there are other point-and-clicks on the store page).
For more mobile-focused stuff, there's
Leo's Fortune, which people seem to be positive towards;
Lifeline, a text adventure that's also gotten some positive impressions;
10000000 and its sequel
You Must Build A Boat are addictive Match-3/RPG hybrid games; I would wholeheartedly recommend 80 Days, but it seems that the version up on Amazon is currently exclusive to Kindle devices; there's also
Framed, an interesting puzzle/action game that involves moving comic panels around;
Wayward Souls is a dungeon-crawler that's been recommended for a long time; same with the addictive puzzler
Threes. Finally, there's the
Kairosoft games, which can be good, though they tend to repeat their genres, with only a different topic (e.g. Pocket League Story, Grand Prix Story, and Pocket Stables basically have the same sports-management gameplay, so I'd recommend picking the one with the topic that interests you the most).
