Watson and Holmes are, of course, the ultimate bromance relationship. A bromance doesn't include sexual intimacy--the inference is that it could.
So, regarding the couples I listed, how much does an undercurrent of romantic feeling or attraction show up between the couples?
David Burke and Edward Hardwicke and Jeremy Brett come across as concerned best friends. In many ways, they capture the English good-old-boys' relationship that could be entirely sexual but hey, it isn't as if anybody is going to say anything, so who cares? Or notices? Or talks about it?
Jude Law and Robert Downey, Jr. deliberately and somewhat self-consciously present a bromance (maybe, it is an American thing--see below). That is, although the movie makes VERY VERY clear that the two have beautiful female significant others, they don't pretend, either, that they don't live in each other's pockets, refusing to be separated.
Ben Kingsley and Michael Caine in Without a Clue: since Kingsley's Watson is employing Caine's Sherlock, the relationship is less bromance and more Andy and Barney though the latter relationship has its own elements of bromance!
Martin Freeman and Benedict Cumberbatch, interestingly, are more like Brett and Hardwicke/Burke than the others on this list. That is, the relationship is very British. They will fight and die for each other; at the same time, they exist on parallel tracks.
The Britishers seem to have a knack for presenting the bromance without feeling any need to draw attention to it--or not. Perhaps due to the lingering public school system, Britishers seem to take the bromance rather for granted.
A number of shows on American television in the 1970s to 1980s used two male detectives. With the exception of Archie and Nero--who are entirely unique--an element of bromance resides in nearly all of them and much was made of the two men being pals. They were replaced within a decade with male-female investigatory partnerships.
