One of the best portraiture tips I have seen (unless you are doing candid or action photos) is to ensure that the subject is looking at, or near the lens. It's amazing how much better portraits look without too much white of the eye in the photo, and it makes you feel more connected to the subject when they're actually looking "at you" in the finished photo, like they're about to introduce themselves. This would be good for profile photos.
Portraiture techniques vary depending on a lot of factors and you could fill volumes on just a few of them. I’ll lend a few tips;
Using a long lens with the aperture stopped down allows you to narrowly focus on the subject and throw the background out of focus, what is known as a shallow depth of field (DOF). My favorite lens for headshots was my Nikor 105mm f1.4 prime, but it has problems and needs repair. The long lens also flattens the features slightly making them generally more pleasing (compare with shooting the same shot with a wide lens).
Focus on the eyes so that features forward and behind (nose and ears for example) and slightly out of focus. This draws the viewer to the eyes of the subject and is analogous to what our minds do while viewing something, i.e. focusing on a detail to the detriment of the rest of the subject. I’ve been in studios where assistants use measuring tapes to get the focus exactly right.
Using available light take full advantage of the magic hour, or the period of time just after and before sunrise and sunset when the light is redder that when the sun climbs up into the sky.
Be cognizant of extraneous aspects of the subject. For example how their hands are placed or the arms, are they natural looking or akimbo somehow, detracting from the composition (got dinged on a project in college on that one).
Do not neglect your composition overall. Many artists will hang their work upside down in the studio for a time so they can get into the composition outside of the subject matter. Or their preconceptions.
Be cognizant of your subjects foibles and insecurities. For example a subject my be sensitive of a double chin which can be rectified by changng the angle.
Modeling of the subject by the light is as or more important than the modeling on a vase, but the same rules apply. If working in a studio do not neglect the extras such as additional fill, or a hair light that highlights the subjects head to delineate it from a background. Often fill lights in a natural lighting environment can be supplemented by something as simple as a sheet or piece of cardboard painted white and placed strategically.
Like many subjects, move close to your subject.
Be aware of anything coming out of the subjects head and being too reflexive in your compositions. Try making it more interesting (again, composition).
Avoid placing the horizon line in the center of your composition, keeping in mind the “rule of thirds”.
Lastly, remember, rules are made to be broken, but you need to learn the rules if you want to be the master breaking them.