In Photoshop. Image>Adjust> then tinker with Brightness/Contrast, Hue/Saturation, and Color Levels...

Convert to greyscale, max out contrast using Curves, Brightness/Contrast or Levels, convert to duotone, set to monotone, pick your color, Bob's your uncle.

building on nightrain's comment...after you've adjusted the contrast then adjust hue/saturation and check "colorize" and then lighten, saturate and select your hue. have fun!

Those may not be photoshopped... they might be original prints using linocut or woodcut or screenprinting techniques.
I can't be of much help when it comes to photoshop as I'm really no good with it, but I'm guessing you would up the contrast, convert to black and white (not greyscale), manually clean it up for sharpness and detail, then somehow flood positive spaces with your desired colour... how to actually execute that, I have no idea.
Or you could try doing some lino or screenprints, for some DIY fun.

import into photoshop, either via scanner or from digital photo. the simplest, quickest and most effective:

go to filter, click on SKETCH, then click on "notepaper".

when slider choices appear, choose image balance "6",
graininess "0", relief "0". (you can play with image balance numbers)

after saving, go to IMAGE and scroll down to ADJUSTMENTS. click on HUE/SATURATION and play with those to make color choice. after satisfied, save and go to
BRIGHTNESS/CONTRAST, where you can increase contrast for the strongest image. SAVE and PRINT.

forgot to add:

i also tried "photocopy" and "half-tone"......both under the SKETCH FILTER. yes, filters are the easy way out, but for a novice, great results....and i think that's how those were done.

It's a fun, monochromatic effect!

If you plan on printing from your inkjet, be forwarned that inkjet colors degrade very quickly, i.e.-- lose color intensity. I believe you can also buy an archival line of inks that might give more enduring results.

Another option to try: Convert to grayscale. Image> Adjust> Posterize, 2 levels. Choose your fill color, select black in image with wand, select similar to select all black in the image, fill. Really works best with a high-contrast original, so you may want to boost contrast first.

To add to wig3000's comment. You often can just save your image as a jpeg on a cdrom and take it to a place where they can print photos from disc. The photopriinting machines don't care that your image is not a photo. That way for a couple bucks (depending on the size of the pictures) you do not have to worry about the image degrading

These are duotones. Photoshop-adjustment-remove color-select ok- go to adjustment again- duotone- select colors

You can do something similar with irfanview, which is free. Convert to greyscale then go to Enhance colours and tweak the contrast and brightness, then increase levels of one of the colours. You need a fairly contrasty image to start with, though.

Duotones use 2 inks-- these only use 1.

I'm a graphic designer. I do this type of thing quite often.
Go to Image>Adjustments>Threshold. Use the slider until you get best results. This will change to a high contrast black white. Then in the layers palette create a new layer. Fill with the color you desire. Change the layer's mode to : Lighten. Any areas that were black with have the color.

Threshold can also be used with a non-destructive layer onto the image; a little more advanced method.

Thank you everybody for the responses! I am excited to try this. Laura

Anyone have any tips on doing it in a program other than photoshop for those of us non-graphic designer types?

If you're a flickr user there's Picnic, they have some "one button" transformations to your photos which are fun to try out. I'm not sure if you can do this exactly but you sure can transform your photos in cool and easy ways there!

If you don't have photoshop, try paint.net. It's a free download and is great.

Duotone mode- select the same color for both layers. Gives the contrast and intensity as in these images.

A different way to do this:

You can convert the image to vector and then just change the color based on whatever your color scheme is. This will give you a very clean image instead of a pixelated one. You can also remove the backgrounds if you want. Vector images are scalable based on a mathematical formulas so you can make your pictures as large as you please.

You can try the free 30 day trial of adobe Fireworks or Photoshop if you don't have a program you use. I'm used to Fireworks so you can use the magic wand tool. I'm not really familiar with Photoshop but I'm sure it does the same thing.

if you are an old school photography fan, you can actually use some non-computerized methods too. a very early photo process called gum bichromate printing mixes photo chemicals with watercolor paint, so the paint color you choose determines the color of the print you make. you can also layer colors and brush away sections of a second color to only show the one underneath. prints are done on thicker fibrous paper (usually gelatin sized paper) and not on slick photo paper.

another process called kwikprint adheres well to slick surfaces, anything from shower curtain plastic to glass. you order kwikprint paints in the color you want to use.