I have had my 6D since May 2013 and I love it! I was all set to buy a 5DmkIII at the time, then I used a 6D and 5DmkIII side by side in the studio and fell in love with my 6D. I was previously shooting with a 50D.
In 2 years of decently heavy use (more than 40K shots) I have found that it's weakest area really is sports shooting, which is what it gets knocked for. I recently started shooting basketball and I'm missing focus here and there. It's hitting about 95% of the time for me. Of course, at least half of those misses can probably be attributed to my lack of experience shooting basketball. I've never had a problem missing focus shooting dance, which I've been doing for ten years. I don't miss focus when I'm shooting in the studio or location portraits. So while it's certainly not a camera for a professional sports photographer, or someone who shoots a lot of fast paced sports, that leaves a whole lot of us who will be very happy with it.
My favorite thing... taking it on a campout, putting a fast prime on there and shooting around the campfire or on a night hike with only flashlights guiding us. The noise levels are manageable enough that your images look like photographs and not watercolor paintings after noise reduction.
I shoot my black cat often with it. Though black cat fur sucks up all the light so I tend to put a 600EX speedlite on there for that.
Have fun and happy shooting! I hope you enjoy your 6D as much as I have mine.