Technically, most Catholic parishes are geographical regions, and all Catholics living in a geographical region are in the geographical parish unless they are registered elsewhere. Canon law states:
As a general rule, a parish is to be territorial, that is, it is to embrace all Christ's faithful of a given territory. Where it is useful however, personal parishes are to be established, determined by reason of the rite, language, or nationality of the faithful of a certain territory, or on some other basis (canon 518, Code of Canon Law).
Nevertheless, unless you are formally registered at your geographical parish, or at another Catholic parish recognized to be a Catholic parish by the local diocese, your rights and privileges as a Catholic could be impacted by the fact that you are not a member of a local parish for the simple reason that you won't be known as a Catholic by a parish community and its pastor. Examples of how lack of registration with a parish can negatively impact an adult Catholic's life include the hindrance of becoming a godparent or confirmation sponsor, marrying as a Catholic, and joining a lay association of a religious order or congregation.