Why is broken weblinks so bad?

Here are some examples of why broken/rotten/dead weblinks is bad for your website:

• It is annoying for the visitors.
• Their existence may cause real damage to your online business
• Their existence may cause real damage to your reputation on the internet.
• Lose some of your existing customer base.
• Negative impact on your website´s rating with major Search Engines like Google, Yahoo, Bing...