Praise be to Allah.

Yes: the Prophet (blessings and peace of Allah be upon him) used to engage in recreational activities, yet his entire life was devoted for Allah, the Lord of the Worlds, as Allah, may He be glorified and exalted, says (interpretation of the meaning): “Say (O Muhammad (blessings and peace of Allah be upon him)): "Verily, my Salat (prayer), my sacrifice, my living, and my dying are for Allah, the Lord of the Worlds” [al-An ‘aam 6:162]. 

His noble life was all for the sake of Allah (blessings and peace of Allah be upon him). As for worship, it was obviously for the sake of Allah. 

With regard to matters other than worship, the Prophet (blessings and peace of Allah be upon him) used to race with ‘Aa’ishah, and he used to joke with his family, treat them kindly and chat with them at night. 

Muslim (670), Abu Dawood (1294) and an-Nasaa’i (1358) narrated from Jaabir ibn Samurah that the Messenger of Allah (blessings and peace of Allah be upon him) would not get up from the place in which he had prayed Fajr until the sun had risen, and when the sun had risen he would get up. They used to chat and talk about matters of the Jaahiliyah, and they would laugh but he smiled.. 

At-Tirmidhi (1990) narrated – and classed the report as saheeh – that Abu Hurayrah said: They said: O Messenger of Allah, you joke with us. He said: “But I never say anything but what is true.”

Classed as saheeh by Shaykh al-Albaani in Saheeh al-Adab al-Mufrad, no. 265. 

Ibn Maajah (144) narrated from Ya‘la ibn Murrah that they had gone out with the Prophet (blessings and peace of Allah be upon him) to a meal to which they had been invited, and there was al-Husayn playing in the street. The Prophet (blessings and peace of Allah be upon him) came in front of the people and stretched out his hands, and the child started to run here and there. The Prophet (blessings and peace of Allah be upon him) made him laugh until he caught him, then he put one hand under his chin and the other on his head and kissed him.

Classed as saheeh by al-Albaani in Saheeh Ibn Maajah. 

It was narrated from Anas ibn Maalik that a man from among the desert people – who was called Zaahir ibn Haraam – used to give gifts to the Prophet (blessings and peace of Allah be upon him), and the Messenger of Allah (blessings and peace of Allah be upon him) would equip him if he wanted to go out (on campaign). The Messenger of Allah (blessings and peace of Allah be upon him) said: “Zaahir is our man of the desert, and we are his people of the city.” 

The Prophet (blessings and peace of Allah be upon him) came to him when he was selling his merchandise, and embraced him from behind. The man did not see him, and he said: Let me go! Who is this? Then he turned to face him and when he realised that it was the Prophet (blessings and peace of Allah be upon him), he placed his back against his chest. The Messenger of Allah (blessings and peace of Allah be upon him) said: “Who will buy this slave?” Zaahir said: O Messenger of Allah, you will find me unsellable. He said: “But with Allah, you are not unsellable”; or he (blessings and peace of Allah be upon him) said: “But with Allah you are valuable.” 

Narrated by Ahmad in al-Musnad (12468 – Risaalah edition); Ibn Hibbaan (5790); at-Tirmidhi in ash-Shamaa’il (239); classed as saheeh by al-Albaani. 

Ahmad (24334) narrated that ‘Aa’ishah said: The Messenger of Allah (blessings and peace of Allah be upon him) said on that day – i.e., the day when the Abyssinians played in the mosque: “The Jews should know that there is room for leisure in our religion. I was sent with a tolerant, monotheistic religion.”

Classed as saheeh by al-Albaani in Saheeh al-Jaami‘ (3219). 

And there are many similar reports. 

Imam at-Tirmidhi (may Allah have mercy on him) included two useful chapters in his book Shamaa’il an-Nabi (sall Allahu ‘alayhi wa sallam), one of which is: Chapter on what was narrated about the smile of the Messenger of Allah (blessings and peace of Allah be upon him) and the other is: Chapter on what was narrated about the way in which the Messenger of Allah (blessings and peace of Allah be upon him) joked. 

A person may sleep or play or engage in foreplay with his family, and if his intention in doing so is good, then he will be rewarded for it. 

Al-Bukhaari (4345) narrated that Mu‘aadh ibn Jabal (may Allah be pleased with him) said: As for me, I sleep and I pray qiyaam, and I seek reward for my sleep just as I seek reward for my qiyaam. So how about the Messenger of Allah (blessings and peace of Allah be upon him)?