Islam not only permits entertainment, it in fact recommends it! Imam Ali (peace be upon him) says in Nahjul Balagha: "The believer's time has three periods: the period when he is in communion with Allah, the period when he manages for his livelihood, and the period when he is free to enjoy what is lawful and pleasant. And the last part is a tonic and refreshing for the other parts."
Every day of a believer's life must have some sort of lawful entertainment. Why has Islam given so much weight to entertainment? A man once came to Imam Ali and said that he has molded his nature in such a way that he does not feel the need for lawful pleasures in life. The Imam replied to him: "For now you do not know. Satan flows in man like bloodstream; you won't even realize when he attacks you." Even the best of pious or religious people lose interest in religion and become astray if they don't reserve a break for entertainment.
Involvement in legal pleasures is an outlet for man's natural instincts, and serves as a balance between the soul and body. Our Nafs (carnal self) can be compared to a pressure cooker which will explode if its steam is not allowed to escape. Every person needs a break from his/her daily regular routine, and if this break is not taken in form of entertainment, then our Nafs revolts. The need for entertainment is more significant in young children. Islam advises parents to explain entertainment guidelines for their children based on the present time. Parents cannot expect their children to have fun in the same manner in which they themselves had in their childhood. Imam Ali has advised parents, "Do not force your children to behave like you, for surely they have been created for a time which is different to your time." Restrictions should be made based on Islamic laws and not on cultural habits.
In selecting the appropriate source of entertainment, we should always keep in mind that it is something that will help our mind and body relax, not something that might be physically, spiritually, or emotionally destructive for us.
So, is it next to impossible to find good lawful entertainment? Not quite. Playing sports can be fun! In fact, it is highly recommended in Islam that a father should teach his son swimming, archery, and horse-riding. It is well-known that gambling, music, and wine are forbidden in Islam, but there are many other diversions or alternatives to these. Except chess and cards, most games are permitted in Islam. Music that is suitable for corrupt gatherings is forbidden, but who doesn't love a sweet melodious voice? Prophet Dawood had a melodious voice, and it is said that people in Paradise will hear him only. So the alternatives are Islamic poetry, like Nasheeds, Qasidas, etc. However, one has to make sure that the type of poetry they choose is not Ghina, and does not contain Haram music. (Please consult your respective Religious Authority for jurisprudential clarification in this matter.) Fine arts can be fun, like, painting, drawing, poetry, but not sculpturing!
You can watch movies or read books that do not have indecent words or images and do not have a misleading message. It should be emphasized here that a drama, movie, or story that is permissible for one person might be forbidden for the other, depending on the mental maturity of the person.
(Did we miss anything? Feel free to share your own suggestions in the Comments below!)
It's very important that we entertain ourselves by following Islamic guidelines. We should try to be flexible and innovative in choosing activities. An intelligent person maintains a well balanced life.