A Bucket of Warm Spit
The Vice Presidency is a strange office. In the US, the #2 is formally useless; his (or her) only official duty is to cast ties at the Senate, and as far I'm aware no veep has broken with the president's instructions on that matter since 1800. Some VPs are included in policy decisions, and some are sidelined, but all depend on unofficial sway and the backing of the big guy in the Oval. Unless, of course, something goes wrong, and then the VP is suddenly the most powerful person in the world.
It's an odd quirk of our presidential system. We share it with a few others, mostly in Latin America and Africa, that based their constitutions on our own.
Most other democracies work under the 'Westminster' model, based on that of the UK, and rely on political parties themselves to pick the head of government. If one dies, another leader can be chosen pretty quickly. Some office-holder might be designated a caretaker, but their job is usually just to ensure the party meets to pick someone new. So the successor usually winds up being the second-most powerful person in the government, regardless of what office that person holds. In the UK, Gordon Brown was obviously heir apparent while he held down the chancellorship. In Japan, currently reeling from the resignation of its PM, there's a heated race underway within the party between the foreign minister and the defense minister.
Other presidential systems designate the holder of some other office - usually head of one of the houses of the legislature - as the number two. In France, for instance, the President of the Senate succeeds to the Presidency; a quick election follows. In South Africa, the President picks a Deputy President from the National Assembly, who has real executive authority.
There are good reasons for keeping the next-in-line in your country in a weakened state: it limits the possibility of contests over leadership, it makes the lines of authority clear, it ensures that a new president has campaigned and been elected (President Ford, who was appointed VP, notwithstanding), and it preserves the separation of powers. An understudy that can only act with the president's authority can't really get in the way.
But it's worth keeping in mind that most other countries in the world expect the heirs-apparent actually to do something while they're on-call in case number one meets with tragedy. The last week's hub-bub must look awfully strange from afar.
