On the one hand, the "smile or die" crowd at the breast cancer support groups sounds insanely creepy. Particularly the part where they've ostracized members whose cancer has metastized because they'll bring the mood of the group down.
Also putting pressure on people to feel happy will often make them feel worse. Depressed people who are shown pictures of happy people get more depressed.
On the other hand, being positive seems to have several benefits from a personal success front:
1) Optimistic people are more fun to be around and are more charismatic.
2) Often things that are worth achieving are really hard. Optimists underestimate the difficulty, and, indeed, continually believe that success is right around the corner. Hence optimists will keep cheerily (and ignorantly) marching onwards long after pessimists/realists have realised that the chance of success is low or it's too much work. This leads to a higher chance of them achieving things.
3) Overoptimism in terms of financial risk was bad societally but not individually - as mentioned in the article people who doubted the stability of derivatives were often fired. People who were optimistic and went with the herd made money all the way along and then were bailed out after the crash.
4) Optimists are less anxious which should (at least theoretically) lead to a reduction in stress hormones such as cortisol. Stress (and cortisol,etc) is remarkably good at prematurely aging you and tearing up your body. Also one would expect reduced anxiety to lead to reduced blood pressure. Given chronically high blood pressure leads to an increased risk of heart attacks and strokes there should be a health benefit there too.
(Of course once you've got cancer 'thinking positive' will probably do very little as you're too far gone).
5) Optimists are less likely to commit suicide, which improves health by default.