So here's what I think I know. A lot of this is based on reading and my own math and not on measurements, I have more time to study than I have money to buy bike parts! Other articles have focused on listing the ratios and shifter pulls and encouraging you to do the math, but the more I play with the idea the more I think that's not really what most people are after.

11 speed cassettes are all spaced the same. This includes both road and mountain cassettes. The road side is pretty well documented and includes all three brands. Some sources claim that the MTB cassettes are wider but that seems to be contradicted by the existence of a few systems out there that can use both road and mountain cassettes... like SRAM Rival 1 & Force 1, and Wolf Tooth Tanpan. Also reinforced by the fact that chain manufacturers don't have different size chains for 11 road or 11 mountain.

10 on down, SRAM and Shimano cassettes have the same spacing but Campagnolo is its own thing.

Shimano 10 and 11 mountain ("Dyna-Sys"), and SRAM 11 speed mountain ("X-Actuation") RD's all have about the same ratio. The 11-speeds give you the capacity for the 40+ tooth cassettes, the 10's are only rated to handle 36. This factoid is confirmed thanks again to the Tanpan, which will work with any of the above. But you can find reinforcement for it all over MTBR, Singletrack, etc. Older SRAM "1:1" RD's have about the same ratio too.

SRAM 10 road and mountain, and 11 road RD's all have the same ratio ("Exact Actuation"). But it's not usefully close to anything else, being squarely in between the road and mountain stuff.

Shimano road 11 speed and Tiagra 4700 10-speed RD's, all have the same ratio. I think this is also very close to Campagnolo's, but this is where my proof is thinnest, because it's based on what I think are rounding errors between other people's tables. That also means that the Shimergo trick could also be a "Shimano-a-mano" trick, where the 11 shifter could run a 9 SIS, and the Tiagra 4700 could run an 8 SIS. Due to the prevalence of Shimano parts this seems like an easy one for some mechanic to try... toss a 4700 brifter on a Claris bike and see what happens.

Older Shimano (road up to 10, mountain up to 9) was called SIS and the RD's all have the same ratio, with an exception for early indexing Dura Ace. So it all works. SRAM MTB RD's that are compatible with this are marked "2:1".

Shimergo is a known trick whereby Campagnolo 10 speed Ergos will run an 8-speed SIS rear, and an 11 Campy will run a 9 SIS. I have the latter running on my bike and the drop-bar mountain bike thread in the C&V section here is otherwise full of them.

Campagnolo had a big change in their RD's in the middle of their 8 speed era and so far as I can learn they've all been the same ever since.

At the front, doubles are really tolerant. You basically set the top ring position with the shifter index and the bottom ring position with the limiter on the derailleur.

Triples are less tolerant. The upper is still set by the index and the bottom still by the limiter, but the middle-top shift is where the problems lie. It seems as though there are two basic families, Shimano road, and Shimano mountain which includes everything else. To detail what I mentioned above I have a Shimergo setup where at the front I have an Athena 11 Powershift Ergo running a SRAM X5 FD and it works just great, the indexes line up well enough. The FD even runs a 53 ring which you really wouldn't expect. The MTB front shifters and FD's are all compatible between SRAM and Shimano. There are also workarounds that don't rely on indexing... some grip shifters have many detents instead of three. Bar-end shifters aka barcons, downtube shifters, and non-Powershift Ergos are all essentially friction on the left/front instead of indexing and can be used with any FD.

Other brands than Campy and SRAM - Micro Shift and Sunrace for example - are pretty much all compatible with the equivalent Shimano product.

A word about chain width... so far as chains know there's really no such thing as a "7 speed" or "11 speed" rear derailleur per se. The internal widths of derailleur chains, set by the rollers and that actually rides on the pulley teeth, is traditionally "3/32" - according to the Wipperman website it's 2.2 mm for 9-10-11 chains and 2.4 mm for 6-7-8 chains. Cog teeth are all 2mm or less, so the chain always has kind of a sloppy fit. And the derailleurs all seem to have plenty of clearance on the outside.

I've spent way too long on this... more later probably