The play is popular because it is humorous and has a happy ending.
A Midsummer Night’s Dream is a story of love, fairies, and mischief. What’s not to like? The play’s universal popularity is largely due to its simple plot—a group of lovers and a group of fairies—that is complicated in a simple way.
There is plenty of comic relief. When Puck trades Bottom’s head for that of a donkey, there is plenty of humor in the puns that follow.
I see their knavery: this is to make an ass of me;
to fright me, if they could. (Act 3, Scene 1)
Ass accuses the other craftsman of making an ass of him when they run from him, when really Puck made an ass of him (literally), because he was making an ass of himself (figuratively) when making a fool of himse.f.
Midsummer Night's Dream is such a popular play because its timeless and has universal themes. The notion of love and unrequited love is very much relevant to people everywhere. Jealousy is also prominent: Oberon is jealous of Titania's love for the changeling boy; Helena jealous of Hermia for having Demetrius's love; and Demetrius jealous of Lysander for having Hermia's love. The play is also incredibly entertaining and humorous: Puck plays tricks on the lovers, the crude mechanicals bumble their way through a play, and there are a slew of puns and banter.