|Well... it is free, as is the Linux operating system on which it runs. So that was a good start. And I've used Linux since the mid-1990s, on machines that run all the time. MythTV is the best-supported Linux DVR and its architecture is as well-thought-out as any of the big Linux players now.
Linux is stable: my first MythTV machine ran 24/7 for 8 of 9 years before I replaced it with something newer. Before I finally shut it down it had been running for over 2 years, on a computer that was already a year old when I got it.
An important thing to understand is that MythTV is built with a client- server model. That makes it very flexible, and appeals to my "collection of good parts" software side. The server (MythBackend) part is in charge of making and manipulating recordings. The client (MythFrontend) part deals with displaying those recordings. In my case both parts run on the same machine (the simplest case), but this need not be so. The Backend can run on a separate machine, perhaps dedicated to your media collection, while one or more Frontend machines can be used to view the collection. The Backend is connected to your TV provider's signal (and the Internet for downloading listings), and your Frontends connect to it via some network connection, either wired or wireless.
One thing that really makes a difference between MythTV and the appliance DVRs is that MythTV does not need to play nice with content providers. Why does this matter? Commercials. The appliance DVRs have to get along with content providers because they help each other. So, it's not likely that any appliance will get commercial detection (nevermind removal) anytime soon. MythTV doesn't have to care, so its commercial detection is as good as a bunch of keen people working on it for free can be. Which is Very Good. This has changed TV-watching for me forever, and probably would for you too.
MythTV is a global effort - it has smart people from around the world working on it, and is meant to be used by people around the world. That wider thinking is good for software.