Q:

What assets would be valuable in a post-apocalyptic scenario?

In spite of the tendency for people to think of gold and diamonds as an emergency store of value for a shit-hits-the-fan scenario, I have a hard time understanding how owning physical gold would actually be of great practical use to me in such a scenario. 
For the sake of argument and to avoid speculating on what this scenario might look like (nuclear disaster, global war, pandemic, natural disasters), let's assume that as a result of some combination of events:

Major stock exchanges lose 80% of their value
Significant portions of the economy simply shut down
Widespread panic results in runs on banks causing them to fail
A shortage of goods and insatiable for currency cause hyper-inflation 
Power, water and sanitation infrastructure fail
You get the picture

My question is, what should you invest in now that would be much more valuable in a post-apocalyptic scenario?

A:

This is going to be a list of some things that will likely be of value immediately after some apocalyptic event.  However, note that I am not answering your question of what you should invest in now to take advantage of such an event.  That is a pretty ridiculous notion.  Preparing oneself for such a possibility is certainly a good idea.  That said, there are some realistic limitations to how you could take advantage of such a situation.  Namely, the very real requirement of physical security.  Unless you have a huge posse -- armed to the teeth -- to defend your cache, someone will come along with a bigger and better armed group to take it.  (Not to mention that I am the type of person that would -- at least -- consider organizing such a group to take you down; if only as a matter of principle.)

Guns & ammo (Also, knives; ideally ones that can be used as weapons and for food preparation/hunting.)

Also, fishing gear and other ways to obtain food.
(Bows and arrows come to mind, both as ways to obtain food and for protection.  However, there is a serious practical limitation.  Arrows (and even bows) are much more fragile and bulky then guns and bullets.)

Alcohol.  Especially liquor.  It's concentrated and easier to store than beer or wine.  Beside for getting inebriated, it is useful as a sedative and antiseptic.
Non-perishable foods.  Canned goods are obvious.  Though, grains and cereals can be stored with relative ease under some circumstances.  (Obviously, not so easily done in an urban area.)
Methods of starting a fire.  Preferably rugged ones, such as flint and steel.  (Lighters would only be of limited use.  Matches are bulky and require water-tight storage.)
Salt and/or salt-licks.  (Possibly, other forms of non-perishable bait.)  As bstpierre puts it, hunting will be about survival not sport.
Hand-tools.
Textiles, fabrics, thread and needles.
Medicines of all sorts, though especially antibiotics, antiseptics and painkillers.
Books of a practical nature.  Topics such as: wilderness survival, cooking, carpentry, etc.

The list is mostly ordered in terms of value & practicality.

Ultimately, I doubt there is much that will provide a practical investment idea for such a scenario.  The physical security issue is a big limiting factor.  In a post-apocalyptic scenario it goes back to who is bigger, stronger and better armed.
One thing does come to mind: knowledge.  Prepare yourself with the skills and knowledge you need to survive in such a scenario and you will be invaluable.  Also, as bstpierre notes in the comments, connections will likely also be important.  (Probably local or nearby connections.)  No one person can do it all alone.  It will come down to cooperation.

A:

Gold and silver are for after the crisis, not during.  Gold and silver are far more likely to be able to be exchanged for things you need, since they are rare, easily divided, etc.
Getting land away from where the crap is happening is also good, but it's more than that.  Say you have land somewhere.  How will the locals view you if you move there to hunker down only when things go bad?  They won't really trust you, and you'll inherit a new set of problems.  Building relationships in an off-the-beaten-path area requires a time investment.
Investing in lifestyle in general is good.  Lifestyle isn't just toys, but it's privacy, peace of mind, relationships with people with whom you can barter skills, as well as the skills you might think you'd need to do more than just get by in whatever scenario you envision.
For the immediate crisis, you'd better have the things you'll need for a few months.  Stores probably won't be supplied on any regular basis, and the shelves will be bare.  Trying to use gold or silver during the crisis just makes you a target for theft.  With regard to food, it's best to get acclimated to a diet of what you'd have on hand.  If you get freeze-dried food, eat it now, so that it's not a shock to your system when you have to eat it.
(Can you tell I've been thinking about this? :) )

A:

Friendship
This is a long term investment but can be very useful during tough times. Be prepared not only to take but to give as well.
Moreover:

it is useful even when no crisis is around
the more you use it, the more it provides return on investment

