The following are a couple of examples of games that make great use of sound effects. These games not only engage the user more, but are also great examples of how you can use sound effects for more than just basic events such as simple user movements or button clicks:
Threes!: This game has faces on the cards, and if you don't do anything, after a few moments, you'll hear the cards making random noises. Also, if you try to slide the cards into a position that doesn't move anything (an invalid move), you will hear one of the cards say "Nope!" It's really cute and is just another way the ambience of the game is upheld through the sounds. Take a look at the UI of the game, as shown in the following screenshot:
Crossy Road: In this game, every now and then, you'll come across a vehicle that's playing music, a police car, or a garbage truck. All of these are fairly rare, but when the player experiences them and hears the extra level of sound, it becomes more enjoyable...