What are the recommended times for performing ghusl?

The following are some of the recommended times for performing ghusl:

Conversion:

According to the Prophet 's (ﷺ) recommendation, when a person converts to Islam, he should be advised to take a ghusl. Qays ibn 'Aasim said,

"I came to the Prophet  in order to accept Islam and he told me to take a ghusl with water and Sidr (Lote-tree leaves). [1]

Jumu'ah Prayer:

In the early days of Islam, taking a ghusl for the Friday congregational prayers was compulsory. Sa'eed al-Khudree (رضى الله عنه) quoted Allah’s Messenger (ﷺ) as saying,

"Taking a ghusl on Friday is compulsory for everyone who has reached puberty."[2]

‘Aa'ishah (رضى الله عنها) related that people would come to Friday prayer from their houses in neighboring villages dressed in dusty wollen garments which emitted bad odors. One of them came to the Messenger of Allah (ﷺ) while he was in ‘Aa'ishah’s home, (رضى الله عنها)  and the Messenger of Allah (ﷺ) said to him,

"It would be good if you cleaned yourself on this day." [3]

From this we learn that Prophet Muhammad (ﷺ) strongly recommended that Muslims who attend the Friday congregational prayer take a complete Islamic bath (ghusl). However, the obligation was later reduced to a strong recommendation. Samurah quoted Allah’s Messenger (ﷺ) as saying,

"Whoever makes wudhu on Friday, it is good [for him], but if ghusl is taken, it is better."[4] 

References:

[1] [Sunan Abu Dawud, vol. 1, p.93, no. 355, an-Nasaa'ee, at-Tirmidhi and Ahmad, and authenticated in Irwaa al-Ghaleel, vol.1, p.163-4, no.128]

[2] [Sahih Muslim vol. 2, pp.163-4 no. 1838]

[3] [Sahih al-Bukhari 902]

[4] [Sunan Abu Dawud vol.1, p. 93, no. 354 and authenticated in Sahih Sunan Abee Dawood, vol.1, p.72, no. 341]