There are more and more devices around the home (and in many small offices) running a GNU/Linux-based firmware. Consider routers, entry-level NAS appliances, smart phones and home entertainment boxes.
More and more people are coming to realize that there is a lack of security updates for these devices and a big risk that the proprietary parts of the code are either very badly engineered (if you don't plan to release your code, why code it properly?) or deliberately includes spyware that calls home to the vendor, ISP or other third parties. IoT botnet incidents, which are becoming more widely publicized, emphasize some of these risks.
On top of this is the frustration of trying to become familiar with numerous different web interfaces (for your own devices and those of any friends and family members you give assistance to) and the fact that many of these devices have very limited feature sets.
Many people hail OpenWRT as an example of a free alternative (for routers), but I recently discovered that OpenWRT's web interface won't let me enable both DHCP and DHCPv6 concurrently. The underlying OS and utilities fully support dual stack, but the UI designers haven't encountered that configuration before. Conclusion: move to a device running a full OS, probably Debian-based, but I would consider BSD-based solutions too.
For many people, the benefit of this strategy is simple: use the same skills across all the different devices, at home and in a professional capacity. Get rapid access to security updates. Install extra packages or enable extra features if really necessary. For example, I already use Shorewall and strongSwan on various Debian boxes and I find it more convenient to configure firewall zones using Shorewall syntax rather than OpenWRT's UI.
There are various considerations when going down this path:
I recently started threads on the debian-user mailing list discussing options for routers and home NAS boxes. A range of interesting suggestions have already appeared, it would be great to see any other ideas that people have about these choices.