I am just about to start playing Skyrim on my new shiny computer and just wondering what mods you would recommend.

Without having ever fired up the game... I was thinking
4GB memory http://www.skyrimnexus.com/downloads/file.php?id=1013 (no longer needed?)
no more blocky faces http://www.skyrimnexus.com/downloads/file.php?id=30
Enhanced night sky http://www.skyrimnexus.com/downloads/file.php?id=85

My aim with those is to make it prettier without taking too much of a performance hit.

Maybe depending on how much 2k textures hammers my GTX 570
flora http://www.skyrimnexus.com/downloads/file.php?id=141
ground http://www.skyrimnexus.com/downloads/file.php?id=2146

EDIT:
Maybe this one to improve the inventory system
QD Inventory http://www.skyrimnexus.com/downloads/file.php?id=667

i am not running any mods atm.. just a few ini tweaks & pretty much all gfx settings on max. looks superb to me as it is!
i'll probably investigate mods & re-check this thread over the xmas holidays. i hope there will be some inventory mods like btmod for oblivion.

multiplayer skyrim mod thats in it's VERY early stages.
http://www.skyrimnexus.com/downloads/file.php?id=3592

The best mod by far is changing characters idle animations to shuffling

Skyrim is just about the only game I've ever purchased that I've been really happy with from the get go. I don't need no steenkin mods, yet.

I agree it doesnt need any mods, but some of the high res texture packs are beautiful.