There are lots of ways to produce this sort of stuff, some requiring more talent than others, but here's is a relatively low-skill way to use Photoshop to producing vaguely similar-looking images.
(One of the things I like about it is that, with the exception of one step, it's all dynamic. I'm a big fan of adjustable, reversible steps that I can come back and tweak later. Running a series of filters and baking it all into a single layer just feels wrong to me.)
First, find a suitable original photo (which you have rights to, obv.). This is just a photo I snagged off the web, which means this man will presumably track me down and kill me at some point.
Chuck this into Photoshop, as the bottom layer. Above it, add a Threshold Adjustment Layer, which will make the image look like this:
Tweak the threshold value (from 0-255) until you find a setting that you like.
One thing you'll notice is that (depending on your source photo), you may be looking at a lot of detail, with little 'crumbs' everywhere. A simple way to chop this down is to make a copy of your photo (above the original) and then use the Gaussian Blur filter.
With the blur filter's preview feature turned on, you can see the effect it'll have on your image before you commit. (This is the one non-dynamic step in this process.)
Next, I chop out the unnecessary background with white. There's lots of ways to do this, but I like a Solid Color Adjustment Layer, using the alpha mask to control where it goes. (I used the magnetic lasso selection tool to build the alpha mask, for the most part, but simply painting white or black on a layer above the source photo works fine too.)
Now, this is okay, but while a lot of the detail is good, his outline has been lost. To selectively control the threshold in parts of the picture, I use a paint layer to adjust it:
Underneath the white mask, insert a new layer, called 'Adjustment Paint'. Set it to 50% Opacity, and set the blend mode to Overlay. (Overlay can be used to both brighten and darken areas in the layers below.)
Painting black or white on this layer (I use a pressure-sensitive brush, but setting your brush opacity to 30% will do more or less the same thing if you're using a mouse.)
Paint black where you want more black in your final image, and white where you want more white. This lets you tweak parts of the picture to control, essentially letting you change the threshold value in specific areas of your image.
This is the adjustment paint layer over the original photo for illustrative purposes: I actually paint with the threshold filter on so I can see how it looks in real time. Yay adjustment layers!
As you can see, this adjustment layer can be really sloppy. As long as it's under the white mask, it's okay to paint into the background.
I chose to darken his outline to make him look a bit more solid against the white; I darkened his gun but left his gloves and face fairly light.
This is the final image, about ten minutes' work in total:
Of course, you can do much more work - it still looks very photographic, and the sleeves in particular are all kinda crinkly. To take it further, you can hand-paint final details over the Threshold, using this approach as an 80/20 starting point.
Here, just for kicks, I've chosen a slightly lower threshold point to make it darker, adjust-painted the face back up, then put a black stroke around the white mask for a slightly more cartoon, cut-out look:
For reference, this is my final layer arrangement: