I'm setting up a home entertainment computer that will be taking in video input via cable and displaying recorded tv, DVDs, live tv, as well as playing music and movies via HDMI to a TV. What Media Center solutions exist for Ubuntu?
Here is some of my preferred apps.
I included this app because you can use it to manage your audio and it can play almost every video formats out there. It is light on the system, simple, and has so many features (see this for example).
Enna is beatyful. It shows the weather and besides audio, photo and video, it supports bookstore.
It is easy to use, support audio, pictures, video, and is "skinnable". See Aeon skin next.
Support for download from torrent and youtube.
Support for music, photos, videos and games.
Can record videos for you.
It has others features like controls over your home lights, doors, security, etc.
As Aenima99x stated, XMBC which is a complete home theater solution with great themes, plugins, massive media capabilites, and overall looks great in your living room.
Another great suggestion is Boxee which can be installed on top of Ubuntu similar to XMBC. Boxee is less configurable than XMBC, but offers great plugins with a fantastic beginning layout, and is a bit more simple to work with.
Lastly, if you don't need a pretty UI for your movies, you can just install Ubuntu as normal and use the Medibuntu Repository to handle all of your media needs. This won't give you a nice skin like the previous two options, in fact it will be just like having a normal computer as a media center, but it contains a lot of great tools for that setup.
Also feel free to use any combination of the above suggestions, and play around with different setups. The links I provided are all great places to get started.