The ribbed tops, especially those from thicker athletic socks, are also great for making sweat-type wrist bands which are useful to catch the water from dripping down to the elbows when kids are brushing teeth, washing faces, or even helping with washing dishes. I usually just snip and roll them up. I don't bother to sew the longer ones.
I used some ladies socks to make leggings for my grandgirls' American girl dolls. They turned out really cute. The ribbed part was for the legs. The heel part is where I cut sock and turned it under to making a casing and inserting elastic. Voila! :)
I use them when moving. Instead of wrapping my glassware in paper i stick them into old socks and stuff the end into the glass. Tube socks work really well for this because you can cut them to size. Also, i put plates and bowls, anything breakable inside of old t-shirts and stack one loose in between.