The title As You Like It suggests that Shakespeare intentionally wrote a comedy that would include many of the themes he expected to appeal to his audience. He was right. This is one of his most popular plays. The Forest of Arden is an enchanted place where life is simple. Duke Senior expresses this theme of freedom, simplicity, and harmony with nature at the beginning of Act 2, Scene 1.
Now, my co-mates and brothers in exile,
Hath not old custom made this life more sweet
Than that of painted pomp? Are not these woods
More free from peril than the envious court?
Here feel we but the penalty of Adam,
The seasons' difference, as the icy fang
And churlish chiding of the winter's wind,
Which, when it bites and blows upon my body,
Even till I shrink with cold, I smile and say
'This is no flattery: these are counsellors
That feelingly persuade me what I am.'
Sweet are the uses of adversity,
Which, like the toad, ugly and venomous,
Wears yet a precious jewel in his head;
And this our life exempt from public haunt
Finds tongues in trees, books in the running brooks,
Sermons in stones and good in every thing.
I would not change it.
The transforming power of nature is one theme. The superiority of a life of simplicity is another. The triumph of good over evil is another. The audience would like to see Oliver repent his mistreatment of his brother Orlando, and so Oliver repents. The audience would like to see Duke Ferdinand repent of his usurpation, and so he too repents.
The theme of escapism is another important ingredient. We would all like to escape from our humdrum routines and our all-too-familiar work and worries. This explains the appeal of books like Thoreau’s Walden, Defoe’s Robinson Crusoe, and such famous children’s books as Alice in Wonderland and The Wonderful Wizard of Oz.
All the best stories in the world are but one story in reality--the story of escape. It is the only thing which interests us all and at all times, how to escape. -Walter Bagehot
Another theme of As You Like It is the theme of adventure. Rosalind and Celia are enjoying a great adventure in fleeing from Celia's tyrannical father. Orlando and Adam are having their own adventure in escaping to the forest. Touchstone is enjoying his adventure by volunteering to accompany Rosalind and Celia. Celia is a timid sort of girl who would never go off on such an adventure by herself, but she feels safe with Rosalind. Rosalind seems to be enjoying the adventure of pretending to be a young man called Ganymede.
Another theme is that of loyalty. Adam is loyal to Orlando, and vice versa. Celia is loyal to Rosalind, and vice versa. Touchstone is loyal to Rosalind and Celia. All Duke Senior's followers are remarkably loyal to him.
The only sour note in the play is sounded by the melancholy Jacques. It might have been that Shakespeare thought this character would provide dramatic contrast with all the other happy campers. He does not really spoil the fun with his pessimism but is actually quite funny. There is a lot of witty dialogue in Shakespeare's plays, and this might be considered another theme: the theme of wit. Shakespeare excelled at writing this kind of dialogue, and it is to be found in all of his comedies.
As You Like It was written to please audiences by giving them what they liked. Obviously, another theme that audiences never get tired of is love--but that belongs to a different question.