The crossbearer’s role is the simplest of the roles upon the altar. However, it is placed above the role of acolyte, as it is the crossbearer who bears the image of Christ. The processional cross is one of the marks of the Pontifical Mass. Indeed, in the older rubrics books, this was almost the only time when the processional cross would appear! At other non-pontifical events, it is the role of the Subdeacon to bear the cross during processions. We saw this during the Holy Saturday Vigil ceremonies, when the Subdeacon led the Paschal Candle into the blackened church.
Now, the cross is quite a frequent occurrence at Sunday Masses, due to its being allowed according to custom.