The reason I love Shakespeare so much is that had his finger right on the pulse of human nature. And because he understood what made human beings tick, it's so easy to make connections between the characters and themes in his plays to the lives of our students.
link it to real life. The more relevant you can make it, the more likely it is you will get buy in.
When you start Romeo and Juliet, for example, you could begin with some writing prompts: have you ever defied your parents? Had a friend or boyfriend that they didn't like? Have you ever done something stupid to help a friend? If it's Macbeth: have you ever done something wrong, even when you knew it was a very bad idea? Have you ever gone against your conscience because of peer pressure? Get the kids to write about these things even before you start talking about Shakespeare. Have a good class discussion about things that they find interesting, then tell them that they've just spent some time digging into some of the major themes of the play. Trick them a little ;)
Once you're further into the play, ask students to work in groups to brainstorm ways that the plot or characters are similar to people or situations in their own lives -- you don't always have to do all of the thinking, and it's far more effective if they do it anyway.
You can also use more modern assessments to gauge your students' understanding of the play. Get them to use tweets, blog posts or other forms of social media to illustrate what they have learned.
Language is usually the biggest barrier into Shakespeare. Students find it difficult and so they give up before they even give it a chance. We have to remember the important step of teaching them strategies for reading Elizabethan English and of using anchor charts while we study a play that they can reference for reminders.
I created some bookmarks that you can download for free to give your students. They can slip them in their books and use them when they need some help. If you'd like create a colourful language word wall, for your students, check this out.
I hope some of these tips can help you get your students a little more excited about Shakespeare. If you'd like to hear some more ideas about how I connect my kids to the classics, check out this post on the TpT blog.