1. Persistent DNS cache using pdnsd (even after reboot because it is on-disk) with a long minimum global TTL. You would imagine this would be a problem, but surprisingly I haven't had any. I've only had to get in once to correct something. You can manually purge a specific domain, and all of them if you think something is wrong.
2. Powerful enough for good OpenVPN settings. Automatically routes through a VPN, and can be disabled for a specific client if needed. The AES instructions (which are on any Intel chip after 2008) help out immensely compared to using just a generic router.
3. Smoother LAN transfers. A cheap gigabit PCIe card (Intel EXPI9402PT - on ebay for about $20) which takes away local transfer rate problems, especially if you have an NAS.
4. Use it as an NAS. It isn't a good idea to mix devices which need good security with non-critical systems, like NAS so be sure about your settings and know what you are doing.
Another cool thing is port forwarding to the remote VPN instance so you can login remotely and check out your network or access any files/media you have on your NAS.
There are more things people can do which give more control and/or better experience, like setting up rate limiting on clients, custom settings for clients with unknown MAC addresses, etc. Traffic shaping is a good one (prioritize specific type of connections over another - example VoIP > Netflix > torrent).
The extra power really opens up the possibilities of what a router can do.
If anyone has any questions, I'd be glad to help out.