Idle games have been very popular recently. One of the games that originated the genre was Cookie Clicker, which I discussed earlier.
The general theme is that initially you get money / gold / points by clicking your mouse. You can use that money to buy upgrades and tools, which lets you automate your progress (and, in Cookie Clicker, increase your CpS).
Other games have taken up the idea from Cookie Clicker, notably Idle Empire, Idle Farming, Idleplex, and many more. You can go check out this page for a whole list of idle games.
The most recent addition to the genre is Learn to Fly Idle. The game is based on Learn to Fly and Learn to Fly 2. These 2 games were rather popular launch games a couple of years ago. In learn to fly idle the central idea is that you have to launch snowballs. After a while you can upgrade and automate your snowball launching. As most idle games, it takes a long time to get good at the game (think an hour or more!). If you have that time and you like the genre, go check it out!