My 9 month old started tilting her head repeatedly to the left (around 5-10 times at a time, touching her cheek to her shoulder). Is this something I should be worried about?

At 9 months old baby is more aware of his/her parts of the body. Perhaps your daugther found a new way to experimental with her body parts and she finds it is fun to do it. I didn't find anything wrong with this and normally young babies will outgrow certain 'habits' very fast. If you do not like her to do it, you can tell her not to do it, and you will be surprised small baby understands what we are talking.