I teach sonnets and Iambic Pentameter before we start to read any Shakespeare. It helps my students to understand the language. They are able to see that Shakespeare changed the word order to help it fit with the meter, and it helps them to see the purpose in that. I also explain to them that characters of higher social classes speak in iambic pentameter, while the lower class characters do not. It helps with character developement.

It might also be helpful to tell students some of the important phrases we now have thanks to Shakespeare. Doing this allows them to see why we still read him and that it's not as pointless as they may think. Some examples of these are "bated breath," "dead as a doornail, "for goodness sake," and many others. Students usually find this very interesting.

I really love the idea of having the students do a storyboard of the different acts of the play or a comic strip.  Along with all the other posts who recommended watching film clips, I also really like the idea of having the students make their own version of a 'movie trailer' for the play.  They could use clips from an existing play or film their own version of the scenes to run together to make an exciting, cinematic trailer, complete with dramatic music and titles.

Great suggestions in previous posts. The key is to do whatever makes Shakespeare seem relevant to your students - building that connection is critical, especially for those with preconceived mindsets that it's ridiculous to spend time studying something written that long ago. Giving them parts in modern English to share in a class read-aloud helps with understanding the plot. Comparing "West Side Story" with "Romeo and Juliet" helps them recognize how Shakespeare's ideas are eternal and can be adapted to other times and characters. A humorous analysis of the colorful descriptive phrases found throughout Shakespeare's writings can help to develop an appreciation of the impact of his language, both in his own time and today!

I find Shakespeare to be quite a challenge for most students. I make extensive use of movies that I show either after reading or during reading. Our students are much more visually oriented than previous generations, so watching something makes more sense for them. Also, Shakespeare meant for his work to be watched anyway.

I always use multiple film adaptations of a play to show students what can be inspired by just the words on the page -- there are no stage notes after all! I also think that watching movies scenes after reading or studying a scene makes the language even more comprehensible and gives them confidence in their own ability to ready and understand when they are reading on their own and aloud in class.

My students read the plays aloud. I think it helps with identification of the character and the ideas which align with them.

Outside of that, we complete studies on the supernatural and witchcraft (helps to get them excited about the plays)--when examining a play like Macbeth. We also act out some scenes.

I think showing different filmatic adaptations work as well. (Also, this helps students to understand different interpretations of the plays).

The above post makes some great suggestions. My wife, who is an English teacher, also takes her students to a production of a Shakespearean play when possible. This helps students remember that his plays are best understood and appreciated in the context in which they were written--i.e., to be performed. If that isn't possible, a film version might work too. 

When teaching something like Shakespeare that can be difficult, I often ask the students to read together during class and send them home with other assignments instead. My students really enjoyed reading the plays aloud in class.  Each day I would list the characters in the section we were going to read and the kids would race to class to get first pick. I would often ask them to rewrite certain scenes in their own words or in modern day language. Occasionally, we would even act out certain scenes with homemade props. They also enjoyed making comic book strips of the play. With my older students, we had a mock trial for Othello. The students really enjoyed trying to prove it was his fault or blame it all on Iago.