How do other professions such as physicians, dentists, lawyers, stockbrokers, accountants, engineers, pilots, nurses, schoolteachers, etc. break down?
Unfortunately I cannot provide many concrete statistics. However, this is what I've gathered from reading around and on this site over the years:
Physicians: 50/50
Dentists: More Republican
Lawyers: Democrat
Stockbrokers: Republican
Accountants: Lean R?
Engineers: Notoriously apolitical and also depends significantly on the type of engineer
Pilots: No idea
Nurses: More Democrat
Schoolteachers: Democrat
Further...
Psychologists: Solid D
Veterinarians: Solid D
Non-profit execs: Democrat
Academia: Democrat
Construction: Republican
Trades (plumbers etc): I don't really know, lean D?
Pharma business: Republican
Maybe the union ones, but blue-collar skilled trades workers in general tend to vote pretty conservatively and have shifted well to the right in recent decades.
http://www.stat.columbia.edu/~gelman/presentations/inequality.pdf (Search for slide with "Occupation")
Eh, that's not entirely accurate. Skilled workers in the building trades, whether they are electricians or finish carpenters or operators, tend to lean towards the Democratic Party. I'd note that the "politics of profession" link only shows that "construction" workers are Republican if they're in management as contractors or foreman. On the other hand, skilled workers tend to be split or lean towards the Democratic Party, which is hardly surprising.
Basically, blue collar workers are a mixed-bag; workers in extractive sectors of the economy have decisively shifted to right. Because these industries contain such a large chunk of blue collar workers, this gives people the impression that blue collar workers as a whole have shifted towards the right. There's an element of truth to this but it's largely hyperbolic to say that the building trades or manufacturing are no longer "Democratic-leaning", they still are.
Keep in mind that most workers in the building trades have experience with Davis-Bacon wages. As a result, they're well aware of the perks and benefits associated with union representative. Because of this, skilled workers who are committed to the building trades tend to have high levels of labor militancy and gravitate towards the Democratic Party. Obviously, this varies from region to region; social cleavages in some Northern metro areas and the South really cut against class-based voting but in the Midwest or the Northwest, most workers in the building trades are pretty staunch Democrats.