Reinforcement learning (and, in particular, bandit) algorithms have been and can be used to solve problems other than games, such as

- [Recommender systems][1] (actually used in practice by e.g. [Netflix][7] or [Microsoft][5])
- [Portfolio optimization][2]
- [Clinical trials][3]
- [Hyper-parameter optimization][6]
- Self-driving cars (although I am not aware of any real self-driving car that uses just reinforcement learning; however, in principle, RL can be used in this context too)

In general, any problem that can be modelled as the maximization of some notion of _reward_, where you need to interact with some environment (with some states) by taking some actions, can, _in principle_, be solved by reinforcement learning. Take a look at [this pre-print paper][4] (2019) for other applications. 

However, note that there are several obstacles that prevent RL algorithms from being widely adopted to solve real-world problems, starting from poor sample complexity (i.e. they require many samples to reach a good performance) or the partial inability to evaluate their performance online without affecting the users.

 [1]: http://rob.schapire.net/papers/www10.pdf
 [2]: https://arxiv.org/pdf/1909.09571.pdf
 [3]: https://www.pnas.org/content/pnas/106/52/22387.full.pdf
 [4]: https://arxiv.org/pdf/1908.06973.pdf
 [5]: https://azure.microsoft.com/en-us/services/cognitive-services/personalizer/
 [6]: https://arxiv.org/pdf/1611.01578.pdf
 [7]: https://netflixtechblog.com/artwork-personalization-c589f074ad76