I have been trying to get similar information.
-downloads of the cliente are unreliable. One user can male multiples downloads, many users can download it just for curiosity and abandon it after waiting a few hours for the chainblock to load
-number of addresses is not indicative as some one explained before me
I want count effective users: Users that have downloaded the client and got 0.001BTC from the bitcoin faucet are not real users, they are just testing or are curious.
I am interested in users that have, let's say, al least a bitcoin.
Given the ridiculously small information that I have found till know, this is my approach:
1) Count users at entry points to the bitcoin economy: exchanges. Mtgox had 72% of the total trading volume till this month were it has go down to 64%. If we knew the number of accounts signed each month we could make an extrapolation of total users. It would be inexact because the volume of trade per user can vary between exchanges wildly, but then I think that users moving more volume are "higher quality" users for my purpose, that is to measure effective use of the currency. Till now I have not found this info, only specific data commented by Mtgox for the last two months
2) Use other stats to estimate rate of growth in number of users, like downloads of client, blockchain.info charts on new users of their e-wallets, this kind of info
About 1) the only inf I have is the published data by MtGox: "The number of new account opened went from 60k for March alone to 75k new account created for the first few days
of April! We now have roughly 20,000 new accounts created each day."
Combining this 60K data point with 2) you are able to guess-estimate the maximum number of accounts created.
3) Count or estimate other effective users born inside the bitcoin economy: miners, traders, goods sellers, users that bough bitcoins directly from other users.
I have only made a rough calculation that I intend to make more precise but my numbers give a MAXIMUM number of effective users of 1,200,000