In my book Light Mind I described acceptance as the heart of mindfulness. Yet I find this is the aspect of mindfulness practice which I am most likely to ignore - so perhaps the question at the top applies to me and not to others.
I have been reading lately about acceptance of anger. On Twitter, Buddhist life coach Sunada Takagi posted a link to Nancy Baker's article on anger on the tricycle blog. In the article she talks about the need to discover "my own particular version of anger."
Later Ms Baker quotes Thich Nhat Han: "Treat your anger with the utmost respect and tenderness, for it is no other than yourself. Do not suppress it—simply be aware of it. Awareness is like the sun. When it shines on things, they are transformed. When you are aware that you are angry, your anger is transformed...Mindfully dealing with anger is like taking the hand of a little brother."
Ms Baker adds: "Perhaps the most important reason for getting to know our anger is that anger is actually a precious energy that becomes anger only when it is caught up in complex egoic patterns."
I could go on quoting from her article but I recommend you read it yourself.