Of the Bard's many themes, connection is one that occurs through many of his plays. The concept of love, connection, community, and friendship is one that apparently fascinated Shakespeare--it threads through most of his plays, and "What is love?" is a question that he returns to again and again, most notably (at least for this post) in Twelfth Night and King Lear.
Twelfth Night has been called an essay on love because of the many forms love takes throughout the play. There is the love of Orsino and Olivia, which is self-gratifying. Olivia goes into mourning for her brother, shunning the company of men--an action that Feste declares as foolish. Why should a sister so mourn a brother, if he's in Heaven? he argues. Olivia cuts herself off, indulging in mourning as a selfish action. Orsino loves Olivia in the same way; when he speaks of his love for her, it is all about how he feels, how he appears, and how he will be loved in return: when he hears of Olivia's mourning, he doesn't express sympathy for her, he declares, "O, she that hath a heart of that fine frame/To pay this debt of love but to a brother,/How will she love when the rich golden shaft/Hath killed the flock of all affections else/That live in her" (1.1.32-6). Malvolio, "sick with self-love" loves Olivia because of what it will bring him, not for her. He is another variation on the self-gratifying lover.
Self-gratifying love in Twelfth Night serves a comic rather than tragic function in that the characters who indulge in it learn from their errors. Neither Olivia nor Orsino get to be with the ones they originally desire, though they do get to love someone--Olivia, Sebastian (since she cannot have Viola) and Orsino, Viola (since she is his friend, Cessario in a maiden form). However in King Lear, the results are drastically different. Lear indulges in a form of self-gratification when he asks his daughters to tell him how much they love him. This desire for affirmation of love leads to the tragic consequences at the end of the play; he rejects Cordelia, the one daughter who did love him, because she said "Nothing" instead of the over-done language Reagan and Goneril employ. However, Reagan and Goneril really do not love their father, and drive him mad.
Self-indulgent love is offset by the pure and selfless love of characters like Antonio in Twelfth Night and Cordelia and Kent in King Lear. All three characters are willing to sacrifice everything for their loved one. Anotonio risks his life for his friend Sebastian by entering Illyria. He gives him spending money and jumps to his defense in a fight (though it was really Viola he defended). Cordelia and Kent give up their social places out of the love for Lear. Cordelia wants to show her father what love truly is--it is not words and measurements, as he perceives--and for it, she is banished, and loses her inheritance and eventually her life. Kent is also banished for speaking up to Lear and trying to show him the folly of his actions, for he acts out of love for Lear. He then disguises himself and returns, risking his life, in order to serve the much abused king. These characters represent Shakespeare's vision of selfless love.
However, most of us fall somewhere in the middle. We love truly, but it is usually don't love purely or completely without motive. Viola shows great love toward Orsino and Sebastian, but she doesn't risk anything, really, when it comes to demonstrating her love. Until she is revealed at the end of the play, she takes no action if it involves revealing her disguise. Thus, Antonio is arrested saving her (thinking her to be Sebastian). Her love is tinged with self-preservation.
These are just a few examples of the visions of love that Shakespeare gives us in these two plays. He demonstrates that love is a complex but vital emotion that we need as human beings; those who do not demonstrate it are somehow less than human, like Goneril and Reagan. And Macbeth, when he begins down the road of evil, loses his capacity to love and his once strong connection to wife as he is dehumanized. Love comes in varied forms, and Shakespeare explores it with complexity and insight into the inner workings of the human mind and heart.