Shakespeare's collective works span virtually every genre and introduce virtually every character archetype that is still used in modern literature and media. His works are brimming with word play, which often has triple or quadruple meaning; often dramatic, philosophical, and comedic at the same time. He was so prolific and such a good writer that there are conspiracy theories that he was actually several different playwrights sharing the same pen name.
Granted it's not as easy to appreciate his works today because of how the English language has drifted over the last 500 years, but what other work of literature from 500 years ago can you even point to as being popular today in its original form?
If you want to give Shakespeare a fair shake from the literary appreciation point of view, try reading an annotated copy of his works that provide context and translate the less familiar turns of phrase. It probably won't make you enjoy reading his works, but it should at least help you understand why he's so revered.
In terms of actually enjoying Shakespeare, well... He was a playwright, not a novelist! His works are meant to be seen on a stage. There are some really good performers out there whose emotivity can help bridge the language gap. Some troupes also tweak the dialog to make it more accessible to a modem audience, but I don't generally like that because they tend to lose the puns or at least diminish the layers or the poetry.