What are the acts of worship that can be offered to other than Allaah?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

The Arabic word ‘Ibaadah (worship) means humbleness and submissiveness.

Sharee‘ah scholars have defined worship as a hypernym that implies all acts and sayings, whether internal or external, that please Allaah The Almighty and that He loves, in addition to disavowing anything that contradicts that.

Thus prayer, supplication, making oaths, slaughter, prostration, kneeling, and fear and hope are considered acts of worship that must be offered only to Allaah The Almighty.  Whoever offers any of these acts of worship to any entity other than Allaah The Exalted has committed Kufr (disbelief) or Shirk (polytheism).   

It was narrated on the authority of Taariq ibn Shihaab that the Prophet, sallallaahu ‘alayhi wa sallam, told of two men from a past nation who passed by people worshipping an idol. They would not allow anyone to pass without making sacrifices to it; however, the two men had nothing to present as an offering. The people ordered them to sacrifice anything, even if a fly. The first man presented a fly to their idol, and thus entered Hell, but the other man told them that he would never sacrifice anything to any other than Allaah The Exalted.  They killed him in response, and he entered Paradise. [Ahmad in Az-Zuhd and Abu Na‘eem in Al-Hilyah] [Al-Haafith Ibn Hajar mentioned that this Hadeeth is authentic] [Ibn Abi Shaybah narrated this Hadeeth in his Musannaf and attributed it to Salmaan Al-Faarisi who could not have known this story except through the Prophet, sallallaahu ‘alayhi wa sallam, because it was about the past. Hence, this is proof that it was truly narrated from the Prophet, sallallaahu ‘alayhi wa sallam.]

Perhaps the questioner intended to ask about the different types of Shirk (polytheism) or Kufr (disbelief) and its definition.

In conclusion, there are several acts of worship and none other than Allaah The Exalted deserves to be worshipped.

Allaah Knows best.