An important thing to remember when choosing a project when you're still a beginning knitter is that your definition of "beginner" may be different than anyone else's. When I was first starting out, I began with a simple scarf and immediately after wanted to jump into something more complicated. My poor scarf wasn't very pretty (I envy you if your first scarf was wearable), but it's around here somewhere under a stack of cowls and mitts and other pieces that don't get nearly enough wear.
Fear not: beginner projects do not have to be simply practice garments made with ugly colors you wouldn't wear!
The projects above all fit under what *I* would call a beginner category in that they require basic skills: casting on, knitting, purling, and joining in the round, but they all have the possibility of becoming cherished accessories you won't want to give away -- or hide. The Foxy Roxy scarf by Wool and the Gang (left) is the perfect beginner scarf that you won't be afraid to wear around. The chunky knit and oversized measure of the scarf make it very fashion-forward (quite unlike the dinky thing I knit myself during midterm exam time my senior year of college). The GAP-tastic Cowl by Jen Geigley (center) is the seed stitched older sister of Foxy Roxy. It requires you to join in the round, but is still knit on large needles for new-to-knitting comfort. Both of these projects could easily be knitted with a chunky, inexpensive blend yarn. The Honey Cowl by Madeline Tosh (right) uses techniques from both of the other projects and would be a great pattern to try out with a more high quality yarn (to reward yourself for knitting the other two, perhaps).
For some beginning to knit reference (and for those of us who need refreshers on the basics), I suggest visiting Karen Templer's blog. She has a great, exhaustive list of ways you can learn including Stitch n' Bitch: The Knitter's Handbook by Debbie Stoller.