If my memory serves me, 555-telephone numbers were very popular to
include in movies a decade or two ago, because, I presume, nobody in real life
had them.  But I think I've seen some real 555-phone numbers around
lately, so I guess this has changed?  Are all possible 7-digit
phone-numbers now being used, except for those that start with a 0 or
1?  (Never mind area-codes or international numbers.)  Nothing urgent
here, just curious. :)

Hello.

The New York Times published an excellent article on this exact
subject in February 2003:
"Personal 555 Number Is Still Mostly Fiction" By MARCIA BIEDERMAN
On Nytimes.com:
http://www.nytimes.com/2003/02/06/technology/circuits/06numb.html?8cir
[free registration is required if you're not already registered there]

As explained in the article, 555 numbers were originally "special use"
numbers for the Bell System and its affiliates.  That changed in 1994
when the North American Numbering Plan Administration, a contractor to
the Federal Communications Commission, began accepting applications
from the public for 555 numbers. Entrepreneurs snapped up many of them
numbers  in hopes of establishing easy-to-remember numbers like
555-TAXI. In theory, 555 numbers should work without respect to area
code. All but 2000 of the 10000 possible 555 numbers have been
assigned now, but not very many of them are actually working yet,
according to the article. The problem has been that a number of local
phone companies won't properly activate them or charge high fees for
doing so.
 

--------

As for the second part of your question...
"Are all possible 7-digit  phone-numbers now being used, except for
those that start with a 0 or 1?"

No, apparently not. 

In addition to the prefixes starting with 0 or 1, those ending in 11
are also not used. 958 & 959 are reserved as test codes. 950 is
apparently unavailable for some reason, as well.

Sources:

"Each area code can have one of 792 possible prefixes, each consisting
of 10,000 numbers (all the combinations from 0000 to 9999). Each
prefix can begin with any number except 0 or 1 and cannot end with 11,
since these are reserved for special service numbers such as 911 and
411. That is why there are only 792 available prefixes."
source: frontieronline: What is an area code?
http://www.frontieronline.com/585/585_FAQs.html#whatareacode


"...Once this effort is complete, NANPA will update its weekly CO code
report that is posted on the NANPA web page and include the
disposition of all codes, limiting the number of unavailable codes to
only those codes that are truly unavailable for assignment (e.g., N11,
555, 950,  Home NPA, overlay NPA(s), test codes 958 and 959)."
source: NANPA Report to the NANC, cached by Google:  
http://216.239.57.104/search?q=cache:Wf-WzRPtp0QJ:www.nanc-chair.org/docs/Mar/mar01_nanpa_report.doc+prefixes++959+%22test+codes%22&hl=en&ie=UTF-8


search strategy:
"555 numbers", "555 number"
"unavailable codes", "area codes", 555

I hope this helps.

Very interesting!  Thanks for the report.