Hello,
I would like to know how many airplanes, ships, tanks and men are
available to the various armies in the world. Possibly divided in to
categories (eg. submarines / air to air fighters / frigates / heavy
bombers etc ...)

If you are willing to pay a lot for it, Jane's have the best data on
your topic, for example airforces:
http://catalog.janes.com/catalog/public/index.cfm?fuseaction=home.ProductInfoBrief&product_id=120

Usually when I see military numbers in newspapers, they have sourced
it from Jane's.

Is it possible that I have to pay 700 GBP to know these informations?
I just need to know how many things a certain army has. (Eg. On the
Italian Navy website they publish a list of all their ships. No need
to pay)

You can probably find this on the web, but it will
take a lot of work.  Check out the Google Answers
Pricing Policy.  Also, there are tons of Jane's books
at the libraries and 1/2 price book stores.  Jane's
is more or less the best source, and would be the
easiest to find.  Your choices are spending a lot
of money on a good resource, spending more on
GA or doing a lot of work.  See if someone finds
something else.  You also realize there are
around 220 countries in the world, so that makes
your question more expensive also as well.