Hard to say... there are several small, fragmental vocal bits of only around two lines especially in TT I absolutely love (mainly the Old English ones like "The Missing" (TT#12), "Sceadufæx" (also TT#12 I think) or "The Call" (TT#12, 15, 16)); my favourite passage on the TT-ST is also supported by vocals, but they rather sound like an instrument instead of singing (TT#17), and the part I like best for the 'singing' (well, more or less) itself isn't on the soundtracks (Éowyn's Dirge from the EE);
So I think my favourite full vocal song is Emiliana Torrini's "Gollum's Song", both because I admire Emiliana's voice and musical work in general and it's also the song with the most emotive or understanding lyrics. In spite of having been some sort of negative surprise for me when I first heard it, I now think it's the most felicitous of all the songs from the movies, though its style is kind of a break compared to all the rest and it doesn't fit in too perfectly where it is; but that's exactly the point, it's a perfect impersonification of Gollum himself. The name is already a warning, but at first sight it's still just irritating, disturbing the harmony (which the song only does in a very gentle way), leaving one unsure what to think of it; then, finally, after a while, one begins to understand a little, to recognize the same feelings elsewhere as well, until ending up completely addicted and unable to get it out of one's head ~~ or so dontgetit
http://www.drawntothefire.com/btvsvid3.html
there u go! theres a really odd video with it (i think its buffy, i dunno i don't watch it), its not the proper lotr video, but the songs the same