On a more NSA-type level:
IF an angency really wanted to know who paid cash for cetrain items (or if they're watching a specific individual) they can compare the stores transaction data and review video imagery from specific registers to get a picture of the person who paid cash. There's also your cell phone & WiFi connectivity data that can be used to determine if your phone was in a certain location at any given time.
There are prepaid cell phones.
To avoid suspicion, one would need to leave a deliberate paper trail. Just use cash for goods and certain services you don't want traced back to you.
Earlier I did research on money laundering. It's not difficult but one must be a meticulous bookkeeper.
Jeanette Isabelle