It might depend on the particular bike rack but yes generally you can remove them by just taking out the pin that goes through the receiver.   You will want to use a locking pin for that reason.  Some of them also fold down or fold out so you can more easily access the rear gate of an SUV or Truck

I have one for a 2 inch receiver that supports up to 4 bikes hanging from arms...think it is a Hollywood brand.  It folds down.  It is steel and quite heavy but for me provided a good price/feature trade off.

I suspect the ones that support the bikes by the wheels on rails are kinder to the bikes but they seem to be quite a bit more expensive.