You can view the most popular games in the App Store. Tap "top charts" at the bottom, then tap "categories" in the upper left corner. Scroll to games. You'll see the top 140 paid games and top 140 free games.
Some I like are:
Trivia Crack
Words With Friends
Gutterball
Ball Hop
PAC-MAN 256
Tetris
iFishing Saltwater Edition
AirSupremacy
WataWaka
Edge EX
Oceanhorn