Which Camera Should I Buy: Part One
Which Camera Should I Buy Part One - Canon EOS 400D or Nikon D80?
Wow, what a big question! At the end of the day, both of those cameras are excellent starter kits. Much better than when I started in 1979 and either would serve you well. What you really need to think about it which manufacturer you intend to stay with and build a good set of lenses that will last you for years.
I used to be "Nikon" as I used to work for them but then converted to Canon when I went digital. Canon, IMO, have the slight edge with technology in regard to their sensors and performance although Nikon still hold a place in my heart. I used to love their lenses and film SLR's.
If you can, get to a store and try both out. It is surprising how different each one feels in your hands and this "personal" feel can play a large part in your enjoyment of photography. Either camera will produce incredible photographs if used correctly. So as I say, decide which route you want to go and then build a good arsenal of lenses over time.
Edit Sept 2021: Time has moved on and my basic recommendation based on the original answer is maybe look at the Canon EOS 90D or the Nikon D7500. Both a little more expensive but they offer so much more bang for your buck!
Of course, we are deep into the mirrorless world now so that adds to the options. Personally, if you are reading this in 2021/2022, it may be time to look at mirrorless cameras. They are quiet/less clunky, they pack more tech inside and are fun!