Use the db_dump program. It is contained in the package core/db (Arch), db-util (Debian, Ubuntu), sys-libs/db (Gentoo, note that here the binary is called db4.8_dump or whatever version you are using).
On some systems the man pages are not installed, in that case the documentation can be found here. By default, db_dump outputs some hex numbers, which is not really useful if you are trying to analyse the content of a database. Use the -p argument to change this.
Show everything that’s in the file database.db:
db_dump -p database.db
List the databases in the file database.db:
db_dump -l database.db
Show only the content of the database mydb in the file database.db:
db_dump -p -s mydb database.db