Act I - Everything hinges on what Hermia will decide to do regarding her father's complaint against her. Duke Theseus gives her three options to consider in three days: marry Demetrius, become a nun, or die for disobeying her father's demands. This is the most important scene in the act because it forces Hermia and Lysander to elope through the forest and drives Helena and Demetrius to fly after them.
Act II - The most important scene in this act is the one that shows Titania and Oberon arguing over the boy Titania is rearing for her deceased friend. When Titania refuses to give the boy to Oberon, he vows the following:
"Well, go thy way. Thou shalt not from this grove
Till I torment thee for this injury-- (II.i.148-149).
As a result, Oberon tells Puck to go get a flower with a love potion to place on his wife to distract her while he steals the boy. Had Oberon not ordered Puck to go get such a magical flower, the potion would not have been used to cause more confusion with the lovers.
Act III - In the second scene of this act, Puck informs Oberon that Titania is in love with Bottom, whose head has been turned into the image of a donkey. This is a very famous scene because it is one of the comedic highlights. The image of a fairy queen loving something so ugly is thought to be hilarious, and it is well-remembered the world over. Puck reports to Oberon the following:
"My mistress with a monster is in love.
When in that moment, so it came to pass,
Titania wak'd and straightway lov'd an ass" (III.ii.6 and 33-34).
Act IV - Oberon steals the boy and awakens Titania while Bottom's head is still in the form of a donkey. Titania's most famous lines then are spoken:
"My Oberon! What visions have I seen!
Methought I was enamour'd of an ass" (IV.i.73-74).
Not only are these lines famously funny, but it shows that Oberon succeeded with his prank against her. Once that is accomplished, he can focus his efforts to blessing the wedding day for the lovers and making everything right by way of the mortal world.
Act V - This is when Bottom and his friends are able to take their places as respectable men by playing for the Duke on his wedding day. It is also one of Shakespeare's funniest scenes because of the use of malapropisms and amateur way the play is presented. Also, the first and only scene in this act, shows that everything between the lovers is fixed as they sit married with the correct partner to watch the play.
Because of the multiple plot line nature of the play, it is difficult to pick out a "most" important scene. Every scene in each act is dedicated to a different plot line which all gets tied together in Act Five. If I were to choose, though, I'd pick these:
Act 1 - Scene 1: Introduction of the basic plot line that causes Hermia and Lysander to run away.
Act 2 - Scene 2: Puck makes the mistake with the love juice causing Lysander to fall in love with Helena...the beginning of mass confusion.
Act 3 - Scene 2: Helena is mad because she believes the men are mocking her. Oberon puts Puck to work fixing his mistake.
Act 4 - Scene 1: All young lovers are in love with the correct person, and two new marriages are arranged.
Act 5 - Only one scene - all for resolution.