Using a tape backup is still a very good method to ensure that your data is safe. There are some advantages to it, such as the ease of taking a copy off-site, and being able to replace the hardware the backup is done on without losing your data.
The down side of tapes, is that both the tape and the drive eventually wear out, and need to be replaced. Also, remembering to change your tape every day is not always done.
These are the places that a network backup can be a good approach. It can be set to automatically run, so there is nothing to remember. Since it typically stores to a disk drive, the life of the backup hardware is extended.
The choice of software to do a network backup is extensive. You can purchase dedicated backup software, of course. However there are several other ways to do a network backup. Depending on what operating systems you have, you may be able to use software that comes with it. Programs such as FTP and rsync, come with many operating systems. They are available for most other ones, too.
Once they are configured, and tested, they offer a reliable alternative to daily tape backups. You should still make periodic backups to a medium that you can take off-site.