A favorite hat of mine, one I literally can make with my eyes closed is the Simple Slouch Hat It requires no brim and has a simple bind off. This is a great project for beginners who know the basics, cast on, knit, knit two together. It goes up in worsted and a size 9 circular needle. KnitPicks has my favorite needles for this hat - Caspian Fixed Circular Knitting Needles, size #9, 16" length.
Another fast cowl to knit is Drop Stitch Cowl. It also takes Lion's Wool-Ease Quick & Thick and #50 knitting needles.
A really quick gift is a coffee cozy. There are plenty of different patterns on Ravelry, simple to elaborate - Ravelry Search for "Coffee Cozy". Here's a really simple one that caught my eye, made out of Bulky yarn - Coffee Cozy. A really nice, more elaborate one found free in KnitPicks - Cabled Mug Cozy Pattern and another by KnitPicks - Cabled Cozies.
