Certainly, the English-speaking world would be much poorer in imagination and culture. His works translated into hundreds of other languages, Shakespeare's influence has touched many other lands, as well. Deprived of the famous lines that have been quoted and requoted for centuries would leave many of us without the edification of sharing in the human experience with one so insightful, consoling, and delightfully entertaining.
Thousands of titles of songs, novels, plays, etc. have been taken from Shakespearean plays. The Sonnets have touched people's very hearts and spirits. The beauty of the language of Shakespeare has also moved millions of people. Not only has this beautiful language enabled many to better express themselves by quoting it, but the pleasure of this beauteous language is immeasurable.
Life without Shakespeare? I think not. Being deprived of his genius would be like life without color or mountains and streams, birds, animals--all that feeds the weary or melancholy soul. Time and time again people turn to the writings of Shakespeare for solace, enjoyment, beauty, expression.... Shakespeare and his plays have so proundly clarified for the uncomprehending of humanity, cheered the heart; his poetry has fed souls and filled ears and eyes with beauty and granted his audiences the oh-so-needed sharing of the human experience.
Victor Hugo wrote, "The human soul has still greater need of the ideal than of the real. It is by the real that we exist, it is by the ideal that we live." Shakespeare has provided the world the "ideal."