If you're wanting to knit something fast for the smaller set, there are a lot of options because things for younger people are smaller than things for adults. So here are a few of my faves for quick knitting for toddlers and beyond.
No one really wants to get socks for Christmas, except maybe my daughter, who loved her Rolled Cuff Toddler Socks and really needs another pair. Socks aren't the quickest knit in the world, I'll grant you, but toddler feet are small, and you can probably work these up in a couple of evenings.
The Simple Striped Hat is a pattern that goes really fast because you're changing colors every two rounds, so that keeps it interesting and keeps you wanting to knit more at a stretch. You could make this a stash buster and change yarns (rather than just colors) every two rounds and it would probably fly off the needles even faster. In reality, though, just about any toddler hat is a quick knit -- and I'm actually working on one right now for my daughter, so I'll let you know how that turns out.
And at the risk of suggesting you knit scarves for everyone, a project that's slightly more involved but absolutely darling is the OXO Scarf. Knit this one to any length for kids young or older, and you can literally wrap your kid in hugs and kisses. What parent or loved on of a child wouldn't want that?