Should I sterilize new canning jars?
You should sterilize your jars and lids before every use.

The dust that gets on them between uses and even in the box is enough to warrant sterilizing.

It doesn't take long. Running them through a cycle in the dishwasher with a steam or sterilization step is enough. I boil the lids in a small sauce pan.

Edit

Debbie M's comment below made me think that some clarification is warranted.

Lids used to need to be heated to soften the seal so it would seal properly. That is no longer the case.

Additionally, bottles and lids don't need to be sterilized if they are going to be processed for longer than 10 minutes or pressure canned.

http://nchfp.uga.edu/how/general/recomm_jars_lids.html

Foods that are processed less should have sterilized jars and lids. I am in the habit of washing them in the dishwasher which also sterilizes them.