I'm searching the absolut amount of hospitals in the US. If it is
possible the number by state and with address

Thank you

Dear elise,

According to data from the American Hospital Association, there were
5819 registered Hospitals in the United States in 2000.

Source:
American Hospital Association, Ressource Center - Fast Facts On US
Hospitals
http://www.hospitalconnect.com/aha/resource_center/fastfacts/fast_facts_US_hospitals.html

Unfortunately, I did not find a list splitting this number by states.
However, this website offers a complete database of hospitals in the
USA, sorted by states, then by names:

Find Hospitals, by HospitalSoup.com, 2002
http://www.hospitalsoup.com/hospitalsbystate.asp

Here is a database with all US hospitals sorted by state, town and
then name:

HospitalDirectory.com - Hospital and Medical Center Search Directory
http://www.hospitaldirectory.com/Hospitals/Directory/Default.asp?Reference=DrDir.HospitalStates&TargetPage=Details.asp&newSession=true

This Website lists all US hospitals on the World Wide Web:

HospitalWeb, by the Department of Neurology at Massachusetts General
Hospital, 2002
http://spauldingrehab.mgh.harvard.edu/hospitalwebusa.html

Search terms used:
"all hospitals in the us" list:
://www.google.de/search?hl=de&ie=UTF-8&oe=UTF-8&newwindow=1&q=%22all+hospitals+in+the+us%22+list&meta=
"american hospital association":
://www.google.de/search?hl=de&ie=UTF-8&oe=UTF-8&newwindow=1&q=%22american+hospital+association%22&meta=

Hope this is what you were looking for!
Regards,
Scriptor