Video? - VLC - Works without any hassels most of the time. And I like it on my windows machine too!
Sound engine? XINE - I forget the other one, there are two main ones or I'm barking made. But That's the one I pick. But never really had hassels with either of them TBH.
Music Library? Amarok. - A few nice features and very easy to use for my needs.
Amarok, hands down. I'd personally recommend version 1.4 though, as 2.0 isn't very mature yet. Amarok is definitely worth the extra RAM required by the KDE runtime IMHO. (Disclaimer: I'm biased. I wrote a very feature-laden script for it and know a couple of the devs )
As much as I love iTunes, after using Banshee, iTunes' playback sounds like complete shit. Banshee sounds way more crisp, *plays FLAC*, and has a better thump.
iTunes? Not so much. Unfortunately, the only Linux box I have now is Warpig -- which is an 800MHz PIII with 384MB of RAM -- and no Sound device D=. So I'm stuck with iTunes (and all of its sexy, iPod-compatible glory -- but at what cost!).
I use Sonata and ncmpcpp as frontends for the music player deamon, which handels playing and the music library. For all other media including soundfiles not in my library I use mplayer.
All other players got way too much dependencies. :>
And VLC now uses qt unfortunately.