A watch cap is my standard go-to knit present. I like to start out by giving everyone one of these, and from there I go to a fancier hat pattern if they seem interested.
This is a super boring thing to knit, but my experience has been that people LOVE them.
I take two strands of Cascade 220, and cast on 72 stitches on #11 circular needles. (Casting on over a larger needle means that the cast-on row won't be too tight or bind.) I then switch to #9 needles and start knitting in 2x2 rib. 52 rounds later I start the decreases, and then you're done!
If you think you might die of boredom, you can add a stripe in a contrasting color. I recommend adding it at around row 40, so that when the brim is folded up it won't obscure the stripe.
These are a popular item to knit, if only because… well, you don't have to mess with the fingers! My two favorite fingerless mitts patterns are Dashing and Stulpen. Dashing is a super-quick knit, and the simple cables give a nice fit. Stulpen is a little more complicated, but the cable is nicely impressive.
The Maine Morning Mitts from Clara Parkes' A Knitter's Book of Yarn are an excellent last minute emergency gift. They are also a great way to use up a single skein of yarn, like Noro Kureyon.
Ornaments and Toys
Although small, these items are often not exactly what we mean when we think of "quick knits." But they make great holiday gifts, and you should have plenty of time if you plan ahead.
I'm smitten by this pattern for tiny sweater ornaments (by Cheryl Niamath, the designer who created Dashing). There are also tons of patterns for tiny mittens, socks, hats, and more. Adorable!
Similarly, there are a ton of patterns for knitting toys. My favorite are the felted knitted amigurumi patterns created by Crafty Alien. Her patterns aren't free, but the cost is well worth it. She includes extensive instructions, diagrams, helpful hints, and more.
Felted Slippers and Clogs
These items are also often well-received as gifts. I have heard more stories of felted slippers and clogs getting worn to death than all other knit items combined. These also give you the opportunity to clear some of the oddballs out of your stash. All those acorn- and tennis ball-sized leftovers of wool yarn can be put to excellent use here!
The Fiber Trends Felted Clogs pattern (pictured above) started the trend. You have to actually travel to your LYS to buy the pattern (so retro!) but it's well worth it. Along the same lines are the French Press Slippers, and Fuzzyfeet (a free Knitty pattern).
Photo credit: Flickr/sarahfelicity