What industries, products, and services are always in high demand
during economic depressions?

Greetings Rook, and thank you for your question.

When the economy moves into recession, output and income fall, leading
to a fall in consumption and investment. Imports also decline. There
are few industries, products or services that prosper in this kind of
environment and would see high demand. The simple fact is that people
just don't have the money to spend.

However, during a depression or recession, the demand for inelastic
goods (goods that will be bought almost no matter what the price)
should not fall a great deal - as long as they remain affordable.
Inelastic goods include addictive products like cigarettes, and also
essentials or necessities such as food and petrol. These necessary
goods will be less affected by price changes than luxury goods like
holidays for example, which are said to be price elastic.

The demand for government benefits and job-seeking services will be
high, as people scramble for employment or look for monetary
assistance to cover the financial gap left by job losses and rising
prices.

To help me with my answer, I referred to 'Economics Third Edition',
Alain Anderton (2000).

I hope this has answered your question. If it has not, please ask for
a clarification.

Anti-depressants?

Consumer goods - soap, toilet paper, shampoo.  Amway and Proctor and
Gamble will never go under during a depression.

At the risk of sounding morbid, mortuaries are quite depression-resistant as well.

But in serious depressions, even the dead can go unburied!

It seems that many people are trying NetMarketing to make extra or
alternative income. NetMarketing is a combination of MLM and
eCommerce.
Some examples are listed here.

http://www.bishart.com/webmasters

The movies are also popular when times are hard.

<b>Caution</b>

Careful, just because a good/service (like theatrical motion pictures
or "films"/"movies") may rise in a depression, it's no reason to
assume the available capacity will be efficiently used or that the
reported operating cashflows are valid.

<b>Example: Theatrical Motion Pictures</b>

For example, in the motion picture distribution business, there is
excess capacity (theaters) relative to profitable operations. Although
movie viewing may rise in a depression (to be determined), this change
in consumer behavior may not translate into profits or finanical
benefits. Need to look at wheher the increased activity translates
into real profits, or whether there exists "limited pricing power" in
a company/industry with high debts.

<b>WorldCom Lessons</b>: Reported utilization rates may be overstated
significantly

Further, as a result of the WorldCom revelations, we learn that the
"expected rise in demand" may be illusory and unsustainable. The
numbers may be an illusion, demand levels fabricated, and the
"audited" information unreliable for planning, oversight, or risk
assessments. Buyer beware, especially when using informatoin from the
US financial reporting/regulatory system. WorldCom teaches us that
those cashflow numbers can even be manipulated, much to the "surprise"
of FASB and those who say, "You can trust the operating cashflows."

<b>Risk Mitigation</b>

I encourage you to review Schilit's "Financial Shenaigans" for a
primer on how the numbers get fudged. Also, check this out:
<a href="http://www.sec.gov/news/speech/speecharchive/1998/spch220.txt">Numbers
Game</a>

To get industry-specific information, there are also warnings in the
UFOC, or Uniform Franchise Offering Circular:
<a href="://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=Uniform+Franchise+Offering+Circular">Franchise
Information</a>