Worsted is a medium weight yarn and many good things can be made out of it. My dishcloths and dish towels are all done in worsted weight cotton. Most scarves and hats are done in a worsted, it is the "journeyman" of yarns. Thinner yarns are used for baby knits, lacy knits and socks etc.
These are two of my favorite worsted weight yarns:
When knitting a worsted weight you would USUALLY use a US 7 to US 9 knitting needle (4.5 to 5.5 mm) and the gauge should come out about 16 to 20 stitches per 4 inches. There heavy worsted yarns sold and their gauge would be different, what I just wrote pertains to basic worsted weight yarn. Remember the weight is not the type and there are worsted wools, cottons, wool and silk blends, more on yarn later.