never. i did once by accident last week, with horrifying results, related to this:
The only time I ever put workers on any auto aspect is to build a trade route, which they did very well in warlords and vanilla. In BTS this option leads tehm to build other improvements once they are done with the routes which can be disasterous (I have caught workers building workshops ontop of towns!!). Now I make my ownt rade routes, then park the workers in thier cities until needs.
the other day apparently i clicked a wrong key and a worker thought i'd told him to "auto trade route", since a sudden a forest preserve at my national park city turned into a farm

! i flipped out, since even tho i never automate them i
do have preserve forests and preserve old improvements checked. he should not have done that even if i had told him to auto-improve things, which i hadn't, i'd only told him (accidentally) to auto-trade-route things. what was he thinking???
i found the offender, and did the alt-backspace to cancel order on all unit types, so that if anybody else thought i'd told them to do that they'd quit too. i mean seriously, i don't even know what key to push if i DO want them to do that *giggle*.
my gosh i was upset. a freaking free specialist gone due to a misclick and then buggy AI worker logic. i didn't have LMA so i went into WB and gave myself back the forest and the preserve, that fixed that. it made me wonder tho, does the game not consider "forest preserve" an existing improvement that should be kept? i swear i had that checkbox marked. then again, it was a forest in the first place and i also had leave existing forests marked. i think the better AI messed up automated worker logic in new and freaky ways.
and don't even get me started on how it changes the tiles being worked in your cities when you adjust the slider. even when you're not using the governor. if i hand-assign the tiles, i want them to stay that way, no matter what happens afterwards. slider rearrangements, nuclear disasters, city growth, whatever, if i fired my city governor then i'm in charge and you ignore him ok? geez!!!!! oops i got myself started, clearly i need to eat lunch.