What are the acts of worship intended for their own sake, and what are their names?

The act of worship intended for its own sake is that which the Islamic law (Shari'a) specifically intended for the individual to perform, and it is not sufficient for them to integrate it into another act of worship, such as prayer, fasting, or Hajj. Such an act cannot be subsumed under another.

As for the act of worship not intended for its own sake, it is permissible to integrate it into another act of worship, examples being the prayer upon entering a mosque (Tahiyat al-Masjid) and the prayer after ablution (Sunnah al-Wudu'). The purpose of these is simply to occupy the space with prayer.

If one combines two acts of worship in intention, and if their basis is intermingling, such as the ghusl (ritual bath) for Friday prayer and for ritual impurity (janabah), or if one of them is not intended for its own sake, like Tahiyat al-Masjid with a fard (obligatory) prayer, then this does not invalidate the worship. However, combining two acts of worship that are each intended for their own sake is not permissible.