Giving birth date
Brazilians find it completely innocuous to give their birth date for mundane transactions. When I asked a clerk at a bookstore why the date of birth was needed to special order a book, he said that "it's required to complete the form" but couldn't explain the purpose and apparently had never given it any thought.
The reason is that there is much less variation in both first and last names in Brazil than is the norm in the USA or Canada. Therefore, they need something more than just the name to uniquely identify a person.
The 30 most common surnames in Brazil (Silva, Santos, Souza/Sousa, Oliveira, Pereira, ...) make up 65% of the population. In the USA, the 30 most common surnames (Smith, Johnson, Williams, Brown, Jones, ...) represent just 9% of the population. Although I haven't found hard statistics on first names, personal experience tells me that there is less variation among first names as well; Maria, José, and Paulo are examples of very common first names.
So if you have several people named Paulo Silva visiting the health club or ordering a book, the birth date helps identify the specific person.