How many Bitcoin addresses are/have been carrying a balance? Bitcoin addresses can be generated at will, and the theoretical limit to their number is high.  Addresses are constantly being generated to receive funds or balance transactions, but they are also being emptied. 

How many addresses are carrying a balance at the moment, and how has this number developed historically? Would this number be a good proxy for the Bitcoin adoption rate?

I'd also be interested in the number of addresses that have been part of transactions during the last x days (i.e. active addresses).

The blockchain contains all necessary data to derive the numbers, so maybe there's even a site that lists/graphs them?
I calculated the answer by starting with Gavin's "bitcointools" and modifying it to track account balances.

Here's what I found.  Each line shows the number of addresses after the specified block was found, at the end of each month.  So the 1st line is saying that after block 2543 was found at the end of Jan 2009, there were 2,439 funded addresses, and all 2,569 were 'active' in January 2009.  The 'active' number is the number of addresses involved in a transaction in the preceding month, and can be bigger than the number of addresses which remain funded at the end of that month.

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
  2543  Jan 2009      2,569     2,439 (94.94%)     2,569  100.00%  105.33%
  5923  Feb 2009      5,975     5,646 (94.49%)     3,447   57.69%   61.05%
  9389  Mar 2009      9,444     8,868 (93.90%)     3,486   36.91%   39.31%
 12831  Apr 2009     12,893    12,125 (94.04%)     3,495   27.11%   28.82%
 16214  May 2009     16,288    15,388 (94.47%)     3,424   21.02%   22.25%
 18450  Jun 2009     18,528    17,543 (94.68%)     2,267   12.24%   12.92%
 20375  Jul 2009     20,456    19,347 (94.58%)     1,973    9.65%   10.20%
 21939  Aug 2009     22,021    20,749 (94.22%)     1,639    7.44%    7.90%
 24098  Sep 2009     24,180    22,647 (93.66%)     2,212    9.15%    9.77%
 26224  Oct 2009     26,311    24,374 (92.64%)     2,231    8.48%    9.15%
 28441  Nov 2009     28,533    26,411 (92.56%)     2,262    7.93%    8.56%
 32489  Dec 2009     32,611    29,827 (91.46%)     4,420   13.55%   14.82%

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
 37493  Jan 2010     37,647    34,342 (91.22%)     5,304   14.09%   15.44%
 43096  Feb 2010     43,329    37,274 (86.03%)     7,009   16.18%   18.80%
 48297  Mar 2010     48,615    40,329 (82.96%)     6,308   12.98%   15.64%
 53875  Apr 2010     57,806    42,688 (73.85%)    10,839   18.75%   25.39%
 58815  May 2010     63,368    44,620 (70.41%)     6,762   10.67%   15.15%
 63561  Jun 2010     69,540    47,011 (67.60%)     7,056   10.15%   15.01%
 71436  Jul 2010     94,992    53,227 (56.03%)    27,957   29.43%   52.52%
 77452  Aug 2010    107,172    55,995 (52.25%)    14,162   13.21%   25.29%
 82997  Sep 2010    120,562    56,490 (46.86%)    16,883   14.00%   29.89%
 88892  Oct 2010    135,952    58,428 (42.98%)    18,921   13.92%   32.38%
 94801  Nov 2010    155,639    60,615 (38.95%)    22,307   14.33%   36.80%
100409  Dec 2010    176,326    65,622 (37.22%)    23,377   13.26%   35.62%

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
105570  Jan 2011    210,243    69,030 (32.83%)    37,989   18.07%   55.03%
111136  Feb 2011    267,542    78,813 (29.46%)    62,381   23.32%   79.15%
116038  Mar 2011    353,093    90,304 (25.58%)    92,321   26.15%  102.23%
121126  Apr 2011    443,112    99,090 (22.36%)    99,144   22.37%  100.05%
127865  May 2011    631,480   132,152 (20.93%)   203,052   32.15%  153.65%
134121  Jun 2011  1,061,590   196,975 (18.55%)   462,886   43.60%  235.00%
139035  Jul 2011  1,548,806   380,056 (24.54%)   531,002   34.28%  139.72%
143408  Aug 2011  1,930,979   487,833 (25.26%)   428,095   22.17%   87.75%
147565  Sep 2011  2,205,926   533,670 (24.19%)   318,294   14.43%   59.64%
151314  Oct 2011  2,411,298   546,269 (22.65%)   241,105   10.00%   44.14%
155451  Nov 2011  2,601,999   553,251 (21.26%)   225,012    8.65%   40.67%
160036  Dec 2011  2,768,500   568,177 (20.52%)   199,879    7.22%   35.18%

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
164780  Jan 2012  2,956,869   580,453 (19.63%)   236,927    8.01%   40.82%
165643  6 Feb 12  2,994,694   583,126 (19.47%)    62,300    2.08%   10.68%


So the number of non-empty addresses has been around 600,000 since September 2011.

As of block 165643, the ten most common values for addresses to store were: 

 0.00000000 (in 2411568 addresses)
50.00000000 (in   40631 addresses)
 0.00000001 (in   35921 addresses)
 0.05000000 (in   22806 addresses)
 0.00100000 (in   22439 addresses)
 0.02000000 (in   18160 addresses)
 0.01000000 (in   13178 addresses)
 1.00000000 (in   11636 addresses)
 0.00500000 (in    9502 addresses)
 0.00000002 (in    7628 addresses)


The next 43 most common values after that were the 43 values from 3 satoshis to 45 satoshis, with between 5472 and 5799 addresses having each value.
I don't know what's special about 0.00000045 and not 0.00000046, but only one other value with a non-zero 8th decimal digit occurred in more than 25 addresses.  That was 0.00000703, which occurred in 101 different addresses.

I also found a bunch of weird looking addresses, which nobody will ever be able to spend from.  http://blockchain.info/address/871a40e5e61b96b6171f1b435788082edadda7a8 shows a lot of transactions sending tiny amounts to human-readable addresses, spelling out paragraphs of text.

As of block 165643, from Mon Feb 6 2012:

        2 addresses have 6 or more figures (100,000 &lt;= x):
            105,258.88 12WmWuSQCgpEkPQTZ4ABijQaz6TCV69ZpE and
            105,555.00 1933phfhK3ZgFQNLGSDXvqCn32k2buXY8a
       70 addresses have 5 figures (10,000 &lt;= x &lt; 100,000)
      740 addresses have 4 figures (1,000 &lt;= x &lt; 10,000)
    6,552 addresses have 3 figures (100 &lt;= x &lt; 1,000)
   66,118 addresses have 2 figures (10 &lt;= x &lt; 100)
   50,638 addresses have 1 figure (1 &lt;= x &lt; 10)
  459,006 addresses have a fraction (0 &lt; x &lt; 1)
2,411,568 addresses have 0 BTC