Let's take a look at each act and all of the scenes in them.

Act one has two scenes, and their purposes are for establishing plot and characters. Scene one introduces us to Theseus and Hippolyta, who will soon be married. Then the lovers enter, and we learn that Lysander and Hermia wish to marry each other. However Demetrius is also infatuated with Hermia, and her father wants her to marry him. Meanwhile, Helena pines for Demetrius.

Scene two introduces the mechanicals, and the play they will perform. While it is important because we meet Bottom, who will soon fall victim to Puck's trickery, scene one introduces more characters and sets the larger plot in motion: Hermia and Lysander will escape in the forest, but Helena decides to tell Demetrius of their plan.

Act two also has two scenes. In scene one, we meet the fairies and learn of the dispute between Oberon and Titania, which is also affecting nature. Oberon has Puck fetch a flower that will make Titania fall in love with the first one she sees, drawing her attention away from the changeling boy. When Helena and Demetrius enter and Oberon sees how Demetrius spurns Helena's affection, Oberon instructs Puck to use the flower on the young Athenian as well.

In scene two, Oberon applies the magic flower to the sleeping Titania. Puck spies the sleeping Hermia and Lysander, and applies the spell to Lysander, who is awoken by Helena and instantly falls for her. In act two, we could argue that either of these scenes are most important: you could make a case that scene one is more significant because it introduces the fairies and the magic that will soon affect the mortals. On the contrary, you could say scene two is even more significant because that is when the magic is put to use.

In the first scene of act three, the mechanicals enter the forest to rehearse their play. Puck transforms Bottom, giving him a donkey's head. He is the first person Titania sees when she awakes, thus falling in love with him.

In the second scene of act three, Oberon is delighted with Puck's trick on Titania and the Athenians—until he observes that Puck charmed the wrong boy. Puck now charms Demetrius, which causes hi-jinks as both he and Lysander pursue Helena, and all four lovers quarrel before Oberon can fix the mishap.

Both of these scenes in act three serve to advance the plot and therefore are significant. We might note that in the second scene, things start to get resolved, and we move toward a conclusion.

There is more resolution and act four scene one, as Oberon seems to regret what he has done to his wife and undoes the spell. Puck also undoes the charm on Bottom. The lovers wake up, and all seems to be well with them.

In act four, scene two, the mechanicals reunite with Bottom and head towards the wedding celebrations. While this propels us into act five and the final scene of the play, we might name the first scene as more significant since more of the conflicts are resolved then.

There is only one scene in act five and therefore no competition for significance. All of the pairs of lovers, including Hippolyta and Theseus, seem to be happy. The mechanicals put on a funny performance, and Puck closes out the story.

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.