- A set of coasters (preferably cotton or wool). These are great for hostess gifts too, and they don't require you to know much about the recipient's tastes.
- Going with the cup theme, you can make a sleeve for a travel mug. For extra insulation, make it a bit big, and then felt it. These are great for people who love having something warm in the morning, but don't want to burn their hands or put a bunch of paper in the trash!
- To make something really special, but inexpensive, get a ball of thread and start making snowflakes! Little snowflakes can be attached to earring findings or made into necklace pendants. Several little snowflakes strung together can make a choker necklace or garland. Of course, larger snowflake are lovely on a tree or in a window. Just don't forget to starch them to make them look nice!
If you want to make something for a young person, you may also consider having something other than what you make be the focal point. For example, the amulet bag to hold an iPod (as Practical Crocheter suggested) might be better received if it also contained a small gift card for downloads. It may seem silly, but giving handmade gifts alongside more mainstream gifts is a good introduction for people who don't know to care about things handmade.