Hmm, it depends on why you’re using them. For athletes, who are building muscle, there is some evidence that it can be helpful to take a protein shake following exercise. The evidence is quite contradictory, so the effect is unlikely to be all that significant. It is very unlikely that it would be detrimental to stop having them though, unless you lacked protein in your diet.
Most of these shakes are based on milk protein (whey or casein), so the likelihood is that you would get similar benefits by including milk or other sources of protein in your diet. When I was pregnant and felt like I wanted to increase my protein intake, I drank more milk; protein shakes are expensive in comparison to milk or milkshake!