Is shakespeare over or under rated?

The initial difficulty with  'getting into' Shakespeare is the Elizabethan language.

One becomes entrapped by the language difficulty which sadly  disallows one to give the  subject the concentration  it deserves.

As a youth I became interested in archeology, mythology, and real history, not the political history (or the way it was taught) at school.  Shakespeare  gave a version of those times but the language spoilt the impact.  Then I learnt to listen to what he was saying.

Shakespeare had never had the personal experience of a medieval battle, but   someone he knew had, and described it to him  complete with the pending terror and the slow breaking of that day, and Shakespeare captured and described it. Henry the Fifth, the night before Agincourt. It's short but filled with menace.

Read it, wrap your coat around you at the darkness , smell the horseshit, and the fear.

Great shame you know to lose all that magic just because of a change of language.

Why does it have to come down to that silly dichotomy? Anyone who knows anything about literature knows that Shakespeare was a genius of the first order. He was arguably the greatest writer of all time, never mind simply being the greatest who wrote in English. That doesn't make him overrated. The terms overrated and underrated are generally employed by people who don't have the ability to formulate a better argument. 

I agree with RWPossum that 1) the Elizabethan English make the plays difficult to understand and 2) the best way to get at least some sense of it is to watch the performance.

I have seen two performances of Macbeth and heard one on audiotape. I found that I had a deeper and greater understanding of the play when I heard it than when I  read it. A more visceral experience too. In the first performance, the actors were dressed in animal pelts. I really got the impression that I was seeing a warriors' world, where one man trusted another at his peril. The other performance was set in the 1960s. The actor playing Macbeth was made up to resemble a type of politician like US president John F. Kennedy: handsome, charismatic, well dressed, great t.v. presence. Lady Macbeth wore a pillbox hat and dress like Jackie did. They weren't supposed to represent the Kennedys, of course, and it was not set in the US, but it took me back so vividly to that time period. Banquo was gunned down with automatic weapons. These people were politicians who literally smiled and stabbed their friends and foes in the back. Recalling the previous version I saw, I thought there was a timelessness about the play of a young, ambitious couple who was going to get what they wanted but couldn't wait for it to fall into their laps. Macbeth believed the witches' bones and rune stones / magic ball and tarot cards. It all turned sour for them. They couldn't trust anyone at the end.  Queen Macbeth lost her sanity and killed herself because her guilt haunted her. The lords deposed Macbeth and killed him, but it seemed in the 1960s version that Macbeth was tired of living. He thought he was cursed that no man from woman born could end his life. It was almost a blessing to him that Macduff had not been "born" but "ripped" from his mother's body.

Up where he belongs IMHO. 

The polymath, scientist, authority on English verse and top of his class in the Maths Tripos at Cambridge, Jacob Bronowski, described Hamlet as the greatest work ever written in English.

A repulsive neckbeard I knew called Gareth, who is in his forties, has never held down a job, lives on benefits, spends his evenings playing with plastic soldiers and lacks the concentration to read even a news article once said 'Shakespeare is sh!t'.

I'll let you decide.

"Shakespeare wrote with a view to causing delight, and if you have any feeling for poetry he will delight you. But if he doesn't you had better let him alone. It is a dismal thing to inflict him upon school children until they hate the sound of his name; it is an insult to him and an injury to them. The opportunity to enjoy him should be offered to them, and will frequently be successful if it takes the shape of performing a play; but those to whom he is merely a bore should be allowed to occupy their time in some other way." - Bertrand Russell

Pretty much sums up my own view. Is he over or underrated? Depends on you and your interests.  

Shakespeare cannot be over-rated. He could do more with a few English words than the entire internet.

His work is repeatedly produced today, all over the world, so I suppose you can say it is 'considered good.'

But it is more than good. It is, as Cogito says, 'without parallel.

Shakespeare's plays are just as relevant today as they were in the 16th century. 

Neither.  His works are generally acknowledged and 'rated' by most intelligent people as being without parallel.  They're works of utter genius.

The plays are performed all the time, all over the world.

By whom?  By you?