Is it obligatory to have wudoo’ at times other than the times of prayer?

There is no daleel (evidence) to say that it is obligatory to do wudoo’ every time one passes wind, urine or stools, so long as one is not going to pray. If you want to pray, then you have to purify yourself, whether that is from major or minor impurity, because the aayah enjoins doing wudoo’ for prayer. Allaah says (interpretation of the meaning):

“O you who believe! When you intend to offer As-Salaat (the prayer)…” [al-Maa’idah 5:6] 

It was narrated from Ibn ‘Abbaas that the Messenger of Allaah (peace and blessings of Allaah be upon him) came out of the toilet and food was brought to him. They said “Shall we bring you water to make wudoo’?”, and he said, “I have only been commanded to do wudoo’ when I intend to pray.” (Narrated by al-Tirmidhi, al-At’imah, 1770; classed as saheeh by al-Albaani in Saheeh Sunan al-Tirmidhi, hadeeth no. 1506). This hadeeth indicates that it is not obligatory to do wudoo’ except when one intends to pray. But there are actions for which it is mustahabb to do wudoo’, such as reading Qur’aan, when going to sleep, etc. 

It should be noted that it is permissible for a person to offer several prayers with one wudoo’, so long as he does not break it. It was narrated that on the day of the Conquest of Makkah, the Prophet (peace and blessings of Allaah be upon him) prayed all the prayers with one wudoo’, in which he had wiped over his socks. ‘Umar said, “I saw you do something which you had never done.” He said, “I did that deliberately, O ‘Umar.” (Narrated by Muslim, al-Tahaarah, 415). 

Imaam al-Nawawi said in his commentary on Saheeh Muslim, this hadeeth indicates that it is permissible to offer the obligatory (fard) and supererogatory (naafil) prayers with one wudoo’, so long as it is not broken. This is permissible according to the consensus of those scholars whose words carry weight. 

And Allaah knows best.