I keep an eye on the multibit
downloads, which are here:https://multibit.org/awstats/awstats.pl?config=multibit.org
In any given month there are:
+ new users
+ people updating their version.
+ people who stopped using MultiBit for whatever reason.
As the downloads for the last few months are roughly constant between 70K and 80K I think that is probably a good indication of total number of active users.
There are also the bitcoind
downloads available here:http://sourceforge.net/projects/bitcoin/files/Bitcoin/bitcoin-0.8.5/stats/timeline
These are "a bit higher" than multibit downloads but not, say, double, so there are probably 100K active bitcoinds. (They might not be running 24x7 so there would be a smaller number of nodes).
There are also a large number of electrum
users. They don't have public download figures, as far as I know. I think Alexa rankings are roughly reciprocal (i.e. double the rank is half the traffic) so, as multibit.org's rank is 96K and electrum.org is 226K then I guess there would be 30K - 40K active electrum users.
There are about 400K blockchain.info
wallets, and about 40K new wallets every month. The number of active users is somewhere inbetween - 100K ? 200K? Let's say 150K.
Then you've got Armory, Coinbase, exchange accounts . . .
Lots of people use more than one wallet so the total number of active users I guess is:
+ more than 100K
+ maybe 250K
+ less than 500K
edit: this misses out mobile phone Bitcoin wallets - I don't have any figures for those.