Which are the 10 biggest companies that provide maps for electronic
car navigation systems (an example for such a system could be
Destinator)  in the USA and in Europe?

It's rather easy as long as there is not a lot of companies that does
it. The 10 biggest, I can't tell you as long as there are not more
than 2 major players in that field in europe and USA.
Namely, they are "Tele-atlas" and "Navteck". As you may have noticed,
most websites uses one of thoses database. Navteck is more expensive,
but datas are more accurates and completes (more countries, more datas
for all countries).

Navteck deliver it's database in the form of DVD. Standard account
include some regulary updates (2 years ago, when I was working in that
field, it was 3 or 4 each years, it must be a lot more nowadays).
The only problem is that the format they use cannot be used as-is, and
you will spend a lot of time only to convert the datas to a usable
thing for servers.

If you need more informations, I can give you more in my email.

Regards,

   Thomas

P.S: I think this is the most accurate answer that could be given

(I see much of this was covered in your past question)
http://answers.google.com/answers/threadview?id=339447

The new name is Navteq.
It was called Navtech, short for Navigation Technologies.
Before that it was Karlin & Collins.

http://www.navteq.com/
http://www.secinfo.com/dVut2.1Ccz.htm

Map Makers in the USA
http://www.gpsinformation.org/dale/mapmakers.htm

Thought you might be interested in this car navigation system
developer (relating to your past question).
http://www.horizonnav.com/
Formerly part of Visteon/Ford, Zexel, Navtech.