The law mostly. Otherwise ownership of companies would be mostly pointless, similar to that of gambling (in that your fate would be mostly random, more so then it currently is).
Your statement about the law is for the most part not true. There's a much more in-depth discussion of this at this older HN posting: http://news.ycombinator.com/item?id=3227980
I agree with you that yahoo should have sold to microsoft, by the way. But the legal duty to maximize value bit is just not accurate.
Says the fact that he was on the board of directors of the corporation (emphasis on the fact that it's a public corporation consisting of shareholders).
Legally, in his role, his responsibility was to the shareholders first.
Directors solely have a responsibility to the corporation. The corporation has a responsibility to the shareholders.
This gets mucky on boards of publicly traded boards because large shareholders can be directors and may have divided loyalties. There are strong conflict of interest policies, requirements of care and so on that are intended to help manage this, but it can be a tough balancing act.
I've served on corporate boards and it can be a tricky place to serve in the interest of the organization, balance all of these requirements and stay true to your own personal sense of purpose. Its also very rewarding work and I recommend it highly to anyone that has the opportunity to participate, even for smaller organizations, non-profits, etc.
Says who?