There are many hundreds or even thousands of religions in the world. Within each of those religions, there is tremendous variation not only in doctrine but in how people interpret and react to various doctrines. Therefore, it is not possible to generalize about "religion" in some overarching and uniform way. One can only talk about the teachings of specific religions.
Lucretius in De Rerum Natura argued that traditional Greek religion taught fear of the gods, and that Epicurus, a purely secular philosopher, drove out fear from people's minds in a way that was even more impressive than the deeds of Hercules in driving out fearful monsters from the land.
Some forms of evangelical Christianity emphasize the importance of the "fear of God." On the other hand, many other religious traditions, including Buddhism and Bahá'í, would emphasize that their proponents strive towards a spiritual peace that cannot be found in purely secular belief systems. Some psychologists argue that religious and spiritual beliefs function as coping mechanisms, helping people through difficult situations such as illness, and thus may reduce fear in so far as people can put their trust in some form of divinity.