Steve Jobs' family and Apple have confirmed to the press that Jobs died today. His family issued this statement:

Steve died peacefully today surrounded by his family.
In his public life, Steve was known as a visionary; in his private life, he cherished his family. We are thankful to the many people who have shared their wishes and prayers during the last year of Steve’s illness; a website will be provided for those who wish to offer tributes and memories.
We are grateful for the support and kindness of those who share our feelings for Steve. We know many of you will mourn with us, and we ask that you respect our privacy during our time of grief.

Below is an official statement issued by Apple. We have a memo from CEO Tim Cook after the break.

We are deeply saddened to announce that Steve Jobs passed away today.
Steve's brilliance, passion and energy were the source of countless innovations that enrich and improve all of our lives. The world is immeasurably better because of Steve.
His greatest love was for his wife, Laurene, and his family. Our hearts go out to them and to all who were touched by his extraordinary gifts.

Tim Cook's memo (via AllThingsD):

Team, I have some very sad news to share with all of you. Steve passed away earlier today.
Apple has lost a visionary and creative genius, and the world has lost an amazing human being. Those of us who have been fortunate enough to know and work with Steve have lost a dear friend and an inspiring mentor. Steve leaves behind a company that only he could have built, and his spirit will forever be the foundation of Apple.
We are planning a celebration of Steve’s extraordinary life for Apple employees that will take place soon. If you would like to share your thoughts, memories and condolences in the interim, you can simply email rememberingsteve@apple.com. No words can adequately express our sadness at Steve’s death or our gratitude for the opportunity to work with him. We will honor his memory by dedicating ourselves to continuing the work he loved so much.
Tim