Esperanto speakers have their own culture, on top of being a "gateway" to the culture of the entire world (inherently more-so than most other dominant languages are). As examples, gufujoj exist, and Esperanto speakers will talk about what would normally be considered extremely touchy subjects without restraint (such as political talk or questions about racism), even if they wouldn't do this in their home country or another language they know.
In general, Esperanto culture places a huge focus on reading, education (especially of news, facts and languages from around the world), tolerance and acceptance (especially of people completely different from yourself). Esperanto speakers are also more prone to being against globalization and culture-washing or throwing away one's native language, meaning that while they want to be able to talk to people they also want those people to "stay unique".
Native Esperanto speakers are people who have acquired Esperanto as one of their native languages. As of 1996, there were 350 or so attested cases of families with native Esperanto speakers. Estimates from associations indicate that there are currently around 1,000 Esperanto-speaking families, involving perhaps 2,000 children. In all known cases, speakers are natively bilingual, or multilingual, raised in both Esperanto and either the local national language or the native language of their parents. In all but a handful of cases, it was the father who used Esperanto with the child. In the majority of such families, the parents had the same native language, though in many the parents had different native languages, and only Esperanto in common.
Esperanto speakers create a makeshift café (whether in a rented space or someone's home), using Esperanto coins or voucher-like items as well as real money to pay for food and drink. Live music, poetry reading, or literature reading are usual activities. This custom arose in 1995 in order to contrast with the more usual custom of after-convention partying at a bar.
Esperanto has had an influence on certain religious traditions (Oomoto, Bahá'í Faith, etc., see Esperanto#Religion). While some Esperantists subscribe to these beliefs, they are not necessarily common, and are certainly not required or encouraged by any Esperanto groups.
Books that are translated to Esperanto are not usually internationally famous books, because everyone can already read those in another language that they know. For example, Natsume Sōseki's "Kokoro" does not exist but several Japanese crime novels, and several Icelandic novels, that have never been translated to English (or any other language) have been translated to Esperanto. One reason for this is that people are actually translating their favourite stories instead of the famous stories, and another is that it's simply cheaper and easier to get the rights to translate a small-time book compared to a famous one.