No.

Immigration checks between Schengen signatories (see here) - which includes some non-EU countries too - aren't mandatory, but can be implemented whenever one of the states wants to.

As regards customs between EU states, you can only be stopped on suspicion of carrying something illegal, not for declaration of goods/duty etc (with some notable exceptions as regards tobacco, alcohol and new member states).

Many countries also have laws which mandate ID being carried on you.