I have not kept track but in my first world I've found around 1,230 dungeons and 440 mineshafts based on the amount of moss stone and rails I've taken from them (each dungeon has an average of 48 moss stone and each mineshaft averages about 300 rails). I've also found all three strongholds by caving (one was first found with Eyes of Ender and again by caving, I do not count using Eyes of Ender in this context). I did keep track of them in TMCWv4 though and found 202 dungeons (including 11 "double dungeons", which generate in place of 1/20 of normal dungeons) and 60 mineshafts over 121 play sessions and 466 hours spent caving.
If TMCWv4 is representative of what I've found in my first world, with more than 800 play sessions so far, then I've found around 1,350 dungeons and 400 mineshafts, which is close to what I've found based on resources taken from them (dungeons are about as common in TMCW as vanilla while mineshafts are more common in vanilla (less common within 768 blocks of the origin); taking into account the fact that I removed about 1/4 of mineshafts by preventing them from generating near dense cave systems I've explored 500, minus some due to their lower frequency near the origin).
Also, while vanilla does not display the number of mob spawners that you've mined I enabled the stats display for them and have mined 2,520 so far - more than emerald ore and a quarter as many as diamond ore; in TMCWv4 I found 453:
maybe hundreds to even thousands of dungeons. been playing since 2011, not as much anymore but back in 2011-2013 i was addicted to finding and farming dungeons, man the glacier seed was so awesome back then with like 15 dungeons around spawn (made many worlds of that seed lol)
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"good night, good luck" -dying light
i think we should all use common sense and logic when we answer and ask a question but always stay open minded
just cause science fails to explain something does not mean its real (afterlife,big foot, ghosts etc..) does not mean its fake try to stay opened mined instead of closed