(Anyone who's seen the following rant before can skip over it. The rest of y'all, pay attention.)
Portraits can be shot at any focal length, depending on 1) what you mean by portrait and 2) what effect(s) you're looking for. Some folks think that candid street snapshots are portraits. I disagree. A portrait is a portrayal of character and (hopefully) not a surveillance or ID or serendipitous photo.
Some good focal lengths for people-shooting with an APS-C camera are ~30mm for full-body shots, ~40-45mm for 3/4-body shots, ~50-60mm for 1/2-body shots, ~70-90mm for head+shoulder shots, and ~100-135mm for headshots. Desired effects may include context (use a wider lens, like ~10-30mm), thick or thin DOF (see below), romantic softness (use a soft lens, or a vaseline-smeared filter, or some careful PP) or whatever -- but serious portraiture concentrates more on lighting than on lenses.
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My favorite people-shooting zoom is an old M42 Sears-Tokina 55-135/3.5 that cost me US$8 shipped. A good modern version would be the DA*50-135/2.8 but it costs about 100x as much.
My favorite lens for serious studio-type H&S shots is an older M39 Jupiter-9 85/2 -- soft wide open, sharp stopped down. Next favorites are a Vivitar-LU 75/3.5 enlarger lens on a focusing helicoid -- very sharp. From my days of shooting multiple formats, I find the best modeling of features comes at about 80/3.5. Or for ultra-thin DOF, I'll screw a cheap Sony VCL-1546A 1.5x tele adapter on the front of my FA50/1.4 (for a 75/1.4 optic) or my Sears-Tomioka 55/1.4 (for an 83/1.4 result). I've tried that on my K50/1.2 also but DOF is WAY too thin at 75/1.2!
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If you don't know the rules of DOF, here they are, simplified:
* For thicker DOF use a shorter focal length and/or tighter aperture and/or further lens-subject distance.
* For thinner DOF use a longer focal length and/or wider aperture and/or closer lens-subject distance.
And you can roughly compare the DOF of two lens settings by simply calculating what I call the DOF index or FL/AP (divide focal length by aperture). The higher the number, the thinner the DOF. So a 50/1.2 has FL/AP= ~42 and a 135/2.8 has FL/AP= ~48. That's right, a cheap average 135 has thinner DOF than a costly superfast 50!
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Now let's put all this together. Before spending money on a lens, figure out what 'portrait' means to you. If it's ultra-sharp headshots and/or street candids, think of a ~90-105mm macro lens. If you want thin DOF on a budget, get a manual 135/2.8, or try my Fast-Fifty-plus-1.5x-adapter trick. If you want sharp torso shots on a budget, get tubes or a focusing helicoid for a ~75mm enlarger lens. If you want maximum flexibility plus sharpness and budget doesn't matter, get the DA*50-135. I'd have to rob a minimart to afford one, so I'll stick with my Sears-Tomioka, thanks.
People will push their favorite 'portrait' lenses. Yes, the Fast Fifties and Seventies and 85s and 90-105 macros are all splendid portrait lenses. So are cheap enlarger lenses, scavenged medium-format glass, and almost anything else -- if used intelligently. I like old no-iris projector lenses with a Petzval Portrait or similar formula, or a Raynox DCR-250 mounted on M42 bellows, for a 'period' look. But remember that the light is more important than the lens.