Does a US citizen need a passport to travel from one European country to another?

I need to travel from Portugal to Italy, but I already used both entries on my dual-entry Portuguese visa. Will I need my passport if I travel round trip from Portugal to Italy?
Include a reference please, thanks.

What is the best way to travel in European countries?

I want to travel to European countries. As there are many countries in this region for travelling, I want to discover slowly one by one. Any suggestion for me to enjoy travelling ? Appreciated if any.

Can you travel from germany to other European countries wih a US Refugee travel document?

I am planning a Eurotrip this xmas and wondering if I can use my Refugee Travel Document to travel from one European country to another. Thanks!