"He likes to touch her."
Translation:Han kan godt lide at røre ved hende.
With or without the 'ved'?: You can have it or not, it can still mean the same - a physical touch. Ie.: Han rørte hende da de passerede hinanden i døren. That was unintentional. Han rørte ved hende da de mødtes i døren. That was intentional! TGFrenchman also has a point: 'at røre' can also mean to touch emotionally. In this case there should never be a 'ved' in the sentence. Therefore the 'ved' has the function of making it clear, that we are talking about a physical touch.