The main reason many people have suspected that someone else was responsible for the works attributed to Shakespeare is that he had a very limited education. Also, very little factual information is known about his life. It is an interesting question and one which will be debated for centuries, but it is impossible to be 100% sure whether it is true or false that Shakespeare was the real author of the works attributed to him. The question does not seem worth debating unless some new evidence is uncovered--and Shakespeare has been dead for almost four hundred years.
This has been a question for generations. Critics fall on one of two (obvious) sides. Some analysts and critics believe that William Shakespeare did write his own works. Others believe that the "works of Shakespeare" were written by other writers of the time. Some have even stated that "his" works were written and compiled by numerous authors/playwrights working together.
Over time, over seventy men have been assumed to have written the works commonly known as those written by Shakespeare. Common authors, or playwrights, which have been stated to have written "Shakespeare's works" are Francis Bacon, Christopher Marlowe, William Stanely (the 6th Earl of Derby), and Edward de Vere (the 17th Earl of Oxford).
Another person who has also been tied to the works of Shakespeare is Queen Elizabeth the First.
In the end, we will never know based upon the artifacts historians currently have. Something new would certainly have to be found to answer the question once and for all.
It is impossible to tell. Like literaturenerd said, historians simply have no evidence or artifacts proving either side to be right.
It is possible that historians will find some evidence showing the truth, though this is not likely as Shakespeare lived about 400 years ago.
If Shakespeare's works were truly not his own, most evidence of this would of already been disposed, or hidden. The evidence, if any, will not be obvious.
There have been many theories about this over the years and recently claims that Shakespeare did not write his own work have gathered pace with the release of the film Anonymous. It has been variously suggested that his plays are the work of Francis Bacon, The Earl of Oxford, or even his own wife, Anne Hathaway. However, there is little convincing evidence to suggest that someone else is responsible for the work.
What is likely, however, is that in the creation of the First Folio of Shakespeare's published works, is that some editing was done. Some parts of the texts bear hallmarks of having been written by someone else. The most obvious example of this would be the speeches of the witches in Macbeth. They are stylistically different to the rest of the play and it is speculated that these were created by Thomas Middleton. The speech of Hecate is, in fact, deemed highly suspicious and so it is often left out of staged productions.
It is my belief that Shakespeare created the majority of the works attributed to him but given the passage of 400 years it can never be 100% certain.