This question has been asked several times, and even the most educated geuss won't answer your question, because Cryptic dosen't publish thoose figures outside their company.
There is a site that claims that the exact number equals around 65 K, however several discussions on this forum, have concluded that the number must be much highter worldwide, because of several factors in the game.
But here are some interesting numbers:
The Captains database has 20 entries on each page, and there are 54635 pages with 20 each, apart from the last, wich has only 2.
(20 * 54635) - 18 = 1092682
Now... To be realistic, lets say that only 1/3 of thoose are actual live accounts
1092682 / 3 = 364227
Now lets be a little sceptical and say 1/4'th
1092682 / 4 = 273170
With a grim attitude this time (1/5 th):
1092682 / 5 = 218536
Lets be nasty and jump to 10'th
1092682 / 10 = 109268
So as you can see, even with a bad attitude we are going for at least 110k players total, so I'd say there is more than enough people going around.
The numbers above have not taken alts into aco****, but even at 1/5'th I believ that it might just be the closest you're gonna come to a reasonable figure for the player base.
the game has been busy with people lately, specially with the reruns, I expect it to be like this for a bit
as for a total? i dont know, hopfully enough to keep Cryptic and Atari happily creating more content for many years