1. One must have Wudhu for prayers, whether they are obligatory or supererogatory. One must have Wudhu when performing Salatul Jinazah (Funeral Prayer). Allah says:
(O you who believe! When you intend to offer As-Salat (the Prayer), wash your faces and your hands (forearms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to the ankles.) (5:6)
It is lawful for the one who does not have Wudhu to make Sujood at-Tilawah(1) or Sujood ash-Shukr(2) because these types of Sujood (prostration) are not part of a prayer, but it is better that one makes Wudhu before making Sujood.
2. One should perform Tawaf while he has Wudhu. The Prophet (peace and blessing be upon him) said:
"Circumambulation around the House of Allah (i.e. the Ka'bah) is (similar to) prayer." (Tirmidthi).
3. Touching the Qur'an. The Prophet (peace and blessing be upon him) said:
"No one should touch the Qur'an except him who is pure." (Nasa'ee).
It is lawful for one to recite the Qur'an without touching it.
Actions for which Wudhu is commendable
1. Mentioning the name of Allah. Al-Muhaajir ibn Qunfudth (may Allah be pleased with him) said that he greeted the Prophet (peace and blessing be upon him) while he was performing Wudhu and he did not answer him until he performed Wudhu and then he answered him. He said:
"Nothing prevented me from responding to you except that I disliked mentioning Allah while I was not in a state of Taharah.' (Abu Dawood).
2. Upon sleeping. AI-Bara' ibn Aazib (may Allah be pleased with both of them) said that the Messenger of Allah (peace and blessing be upon him) said:
"When you lay down to sleep, perform Wudhu as you perform it for Salah, and lay down on your right side..." (Bukhari).
1) Sujood at-Tilawah: is a Sujood which is done after reciting a verse which necessitates a prostration. There are 14 ayaat (verses) in the Qur'an that necessitates this Sujood. It is not compulsory to make this type of Sujood, rather it is praiseworthy.
2) Sujood ash-Shukr: this type of Sujood is done when Allah graces him with an apparent bounty or ni'mah, the slave expresses his extreme gratitude to Allah by making prostration or Sujood.