How can I check how many total bitcoin users there are?
It would be interesting to track how quickly the user base is growing.
That's the thing with a pseudonymous digital currency where each user has zero, one or many pseudonyms -- it is darn hard to measure.
And even if you knew how many users of the bitcoin software there are, those using an eWallet such as MyBitcoin and those using bitcoin only on the exchanges such as Mt. Gox won't count individually in those numbers either.
Here are some metrics however:
Map showing IP addresses and locations where bitcoin nodes are running
Node counts http://smsz.net/btcStats/accepting
That snapshot shows:
1,317 have their firewall configured to allow incoming (or now with the latest client have UPnP enabled) and are running bitcoin software (or have run in within the past hours. A total of 6,989 nodes have been announcing themselves and relaying transactions. This 6,989 number is easy to spoof however.
There are about a 1,000 downloads of the bitcoin client each day now (average over past 30 days): http://sourceforge.net/projects/bitcoin/files/Bitcoin/stats/timeline?dates=2011-04-10+to+2011-05-09
Trends, rather than actual totals are easier to measure:
Real-time stats as far as transactions, trades, and mining (block generation): http://bitcoinmonitor.com
Volume of trading on the leading exchange (this view is of volume in terms of USDs traded, not BTCs): http://bitcoincharts.com/charts/mtgoxUSD#rg90zigDailyzvzcvzm1g10zm2g25
Alas, the real metric that matters, in my opinion, is likely going to take some method of analysis to provide a meaningful result -- that being the amount spent / transaction volume. Because most transactions have a change transaction it is difficult to know the actual amount of bitcoins spent. For instance, a transaction where there is a 112 BTC input and two outputs, one at 2 BTC and the other at 110 BTC -- how much was spent? Because we don't know which one was the change, picking the wrong one could result in being off by a factor of 55, in this particular instance.
And that number could be spoofed as well. Someone can send their 10K BTC back and forth between two of their wallets all day. The result will be huge volume ... but there was no real spending occuring. One method proposed was to compute each transactions "days destroyed" as the result of the spending, which seems would yield some very good metrics. Though it has not been developed, or at least not shared publicly that I know of: http://bitcointalk.org/index.php?topic=6172.0