What are the typical recurring themes in Shakespeare's plays?

There are many different themes running through each individual Shakespeare play but here are some of the most common and most recognisable and you can apply at least a couple to whichever Shakespeare play you are studying. 

Power

Most, if not all, of the plays include some kind of fight for power. Whether it is political power (such as in Richard III) or power within families (there is alot of this in King Lear). Just look at who is fighting for the power, who they are fighting it for and how those characters are portrayed (evil, heroic, mad etc.)

Nature

Nature can primarily refer to the immediate, physical nature around us, such as in a pastoral comedy like As You Like It (in this play look at how the forest community is contrasted with that of the court). However it can also refer to human nature (such as the Nature vs Nurture argument in King Lear) and the nature of the society that we live in (Macbeth).

Love and Relationships

This is a BIG one as it is a theme examined in pretty much every play. There is romantic, irrational love (an obvious one - Romeo and Juliet, but also Hero and Claudio in Much Ado About Nothing), dutiful and tactical love (King Lear), mix-ups in love which could show the sometimes fickle nature of it (A Midsummer Night's Dream, Twelfth Night) and even love that goes unrecognised by the characters until the very end (Benedict and Beatrice in Much Ado About Nothing.). These are just some of the forms of love in Shakespeare's plays but chances are you can apply it to a lot of the situations that occur.

Conflict

In a lot of Shakespeare's plays, there is physical conflict as the History plays (and some of the Tragedies such as Julius Caeser) actually tell the story of real battles. However, conflict can also be applied to conflict within families (Again, King Lear - there's lots of themes within this one! - but also Romeo and Juliet with the family conflict ultimately causing the tragic death of their children), conflict between lovers (Much Ado About Nothing) or even just emotional conflict (Hamlet). 

So these are just a few of the big themes and hopefully you can apply at least one or two to the particular play you are studying.