I've been on the Kungsleden and surrounding trails twice. I'm headed back this February to Ski it again. I'll be going south to north (Hemavan to Abisko).
As mentioned by others the northern portion of the trail is popular between Abisko and Kebnekaise and out to Nikkoluokta. If you can, I think it is worth climbing Kebnekaise, it's a pretty good day hike if you take your time.
From Kebnekaise (or Sinji) to Saltoluokta is a little less popular and very nice. Most people hike to Vokkotavare then shuttle to Kebnats and boat to Saltoluokta.
Saltoluakta to Kvikkjokk was one of my most favorite parts of the trek, simply because of the lakes, mountains and trees. (born and raised here in Alaska, it reminded me a lot of home) If you get to this area you should really climb up to Skerief.
Kvikkjokk to Jakvikk and thru to Ammarnas is really unsupported, however there is a trail and it is clearly marked with winter x-country sking and snowmachine signs.
There are no STF huts in that section any longer, and the terrain isnt so appealing (to me) Most people bus around it now from Kvikkjokk to Ammarnas.
I go through it for two reasons, I like being able to say I completed the entire Kunglseden and it is difficult.
From Ammarnas to Hemavan is pretty straight forward, I bypass Aigert and follow the lake to Servestugan and continue on to Tarnos then Syters and Viters and eventually to Hemavan.
You can visit my site at www.i907.net and in the photo gallery I have images from my treks in September and again in February.
I love winter camping and trekking, I grew up with it here, and like I mentioned... I'm going back in a few months.
Feel free to email me dan (at) terra trekker (dot) net if you have any questions.
Have a great time!