According to United Bicycle Institute:

1. Determine Maximum Chainring Difference by subtracting the number of teeth in the smallest chainring from the number of teeth in the largest chainring
2. Determine Maximum Cassette Cog Difference by subtracting the number of teeth on the smallest cassette cog from the number of teeth on the largest cassette cog
3. Determine Total Drivetrain Capacity by adding Maximum Chainring Difference to the Maximum Cassette Cog Difference
4. Record the Maximum Cassette Cog (the number of teeth on the largest Cassette Cog)

For Shimano:

SS - Short Cage Road Double - Maximum Cassette Cog is 27 and Total Capacity is 29

GS - Medium Cage MTB/Road Triple - Maximum Cassette Cog is 34(MTB)/27(Road) and Total Capacity is 33(MTB)/37(Road)

SGS - Long MTB - Maximum Cassette Cog is 34 and Total Capacity is 45

For SRAM:

Short - Maximum Cassette Cog is 34(MTB)/28(Road) and Total Capacity is 32(MTB)/31(Road)

Medium - Maximum Cassette Cog is 34 and Total Capacity is 37

Long - Maximum Cassette Cog is 34 and Total Capacity is 45

For Campagnolo:

Short - Maximum Cassette Cog is 26 and Total Capacity is 27

Medium - Maximum Cassette Cog is 29 and Total Capacity is 36

Long - Maximum Cassette Cog is 29 and Total Capacity is 39

NOTE - THIS INFORMATION IS SUBJECT TO CHANGE BY MANUFACTURER

so that is a good general rule but how far have you stretched it and gotten away with a larger cog?
Today I had a buddy over to convert our old 90s race bikes into something we could use daily on the bay area hills. I set him up with a 9speed deore XT dr with a 34t, and I happen to have this unicorn of a dura-ace gt that I set up with a 30t on my 8 speed. and it worked but its close.. may.. maybe could go to 32.....

I have a 6700 short cage with a 12-30 cassette and 50/34 in front.

Not a big stretch. Per Shimano max cog is 28, max total difference is 33. So I’m 2 over on the cog and 1 over on the total. Works fine, I’ve been using this since June 2014 and have over 30,000 miles on it. B screw is pretty much maxed out.

This is an area of specialty for me. I've never met an RD that couldn't do 14-30 on back, but there's a ton of factors that weigh in, of course: chain length, chainring size and difference between big/little chainrings, chain stay length, RD hanger/claw length.

That DA above looks like to could stretch out a LOT more than it is in the photo. Take out a link pair and jump up another two (or probably four) teeth on the big cog.

MTB derailleurs have a few links of wrap to spare so they can do their rated capacity on a full suspension bike.

The later 9 speed and 10 speed MTB derailleurs could do 40t in a 1x but the medium cage versions (like Zee) didn’t have the wrap for it except on a hard tail. The 1x11 derailleurs are rated for 46-47t but get pushed to 50t... and it’s a chain wrap problem again.

The axle position in horizontal dropouts and B-screw adjust will also allow a gain in maximum cog size, though often at the expense of shifting performance, especially with indexed systems.

wolftooth hanger extender might help.

The distance between the axle and rear derailleur mount can vary by dropout, and is completely out of Shimano's control, which is another reason why their specs have to be conservative. The old Campy NR derailleur wasn't rated for a 28T cog either, but some people have made it work.

By pulling the wheel to the rear of the drop outs, I was able to cram a 6 speed 28t into my Legnano, and the old steel Gran Sport Campy seems happy with it. Has anybody ever tried a Wolf Tooth Roadlink extender with an old Campy setup?

I like to use Disraeli gears to determine if my RD is in the ballpark, it recently helped to figure a Suntour Cyclone II GT would work with a 34T cog and hence a shimano Mega range FW. and it worked in the real world too

FWIW

when pushing limits always make sure big big works (I know this from experience....fortunately at slow speed)

With my last 2 build one modern, one vintage, I have grown to like the small/small sizing method. it gives the max amount of chain without over stretching the derailler. My go to guy at the LBS says this is what shimano tech recommends..... but that seems to change over time

This has the added advantage on a full suspension bike that it can be done without deflating the suspension as you'd need to with L/L

I saw these and also the sunrace version- simple idea to just get you an extra 2cm and a few more teeth! anyone using them? I had no idea they existed until last week.

maybe I am being too conservative. it was a 23t so jumping to 30 seemed like a giant step.

If I understand it correctly, the Wolftooth device allows you to use a larger cog than normal, but doesn't increase the derailleur capacity--that is, it doesn't provide any additional chain wrap. But if you're just looking for a lower low, that may be enough.

That makes sense, as largest cog capacity is a function of the length of the derailleur body/parallelogram, whereas chain wrap (capacity) is a function of the length of the cage.