Definitely going to have to go with Tamriel Rebuilt. Anyone who's played with it installed should know why. And for second place the MCP takes the spot not because of it's many bug fixes, but because of it's making the map accommodate TR.

Vivec Expansion v2 or Journals/Writing Enhanced.

For me it's Emma's http://lovkullen.net/Emma/kids.htm

If I use only one mod it will be a head/hair mod for my character. But that is a necessary mod. My favorite mod will always be Children of Morrowind.

Morrowind's Stupidest Criminals. =D

Another mod that kind of blew me away when I found it was Hoghead the Horrible's http://planetelderscrolls.gamespy.com/View.php?view=mods.detail&id=1534.
In spite of the fact that it is quite a few years old, it hasn't "dated" in the way that many inevitably do. If anything, today's computers are able to do it justice in a way that a 2003 machine probably could barely cope with.
And what a difference it makes to Vivec - it suddenly becomes the city that it was always meant to be, complete with shanty towns built on walkways over the water, house-boats and pick-pockets. I just love it.

Morrowind Graphics Extender
Better Bodies
Better Heads
Morrowind Visual Pack
Darknut's Greater Dwemer Ruins Volume 1

'Tis impossible to choose just one, but I can narrow it down to these:

http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=8707, for immersion;
http://www.elricm.com/nuke/html/modules.php?op=modload&name=Downloads&file=index&req=viewdownloaddetails&lid=1946 and http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=2647, because they allow my character to have "a voice"; and
http://lovkullen.net/Emma/Kateri.htm, for unparalleled awesome-osity