Just ticked over 6,500 here (Ben Harper & The Blind Boys of Alabama; Picture of Jesus).
I’ve got 3,270, but I’m still running trial.
I’ve been known to loop the queue a few times while I’m burning in a new amp. 
4700 but I lost the count when I swapped to my NUC as I wasn’t worried about keeping meta edits… Don’t know where it was before then!
6,184
A lot of times I just put music on while i’m doing stuff around the house and just let radio do its thing.
6,767 for me (corrected from the 8,000 I thought it said earlier).
Perhaps it’s infinite…
Whatever the limit its long overdue a bit of local caching. 
I can’t wait for the ‘you haven’t played anything yet’ box to bugger off.
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I’d never even thought to look til I saw this thread… 10,579 and growing…
Ahem, just double-checked mine and it’s actually 234,738… Uh. Honest.
Since the beginning of May there have only been around 350,000 minutes so that’s about 1.5 mins per play you must be not sleeping and listening to multiple zones at once 
I have only 1856 but that’s since some time in December when this database started.