Do you want to turn this…

into this?

For Banality Man, I wanted the backgrounds to look like Pop Art silkscreens. I figured since the campy 60s Batman is one of the game’s design inspirations, doing something kind of Pop-Art-lite would fit the theme. (I’m also a fan of the Pop Art style in general, and in particular consider the Who’s The Who Sell Out one of my straight-up favorite albums of all time.)
A lot of the preset filters that you can use to distort photos in GIMP are pretty good, but if you want to really control the color scheme, it’ll take a little extra work.
After re-sizing the image to the dimensions I needed, I started by using GIMP’s “Cartoon” filter, which is a pretty cool effect all by itself:

The problem, though, is that because my sprites have black outlines, I can’t have a background with so many black lines in it.
This is easy to fix, though. Just use GIMP’s Select By Color tool and be sure to click on a black pixel in the picture. (You may have to adjust the threshold, depending on how thick you want your outlines to be.)
Once you’ve selected all the black in the picture, switch over to the Bucket Fill Tool and choose a color that you want to replace all the black (in this case, I wanted pink). You need to make sure the bucket is set to “Fill Whole Selection” rather than “Fill Similar Colors.”
If everything goes well, it’ll look like this:

Now comes the one potentially time-consuming part (depending on how meticulous you want to be), although it’s still much faster than drawing something from scratch. Switch the paint bucket back to Fill Selection, adjust its threshold, and begin using it to change the colors of the rest of the image. (You’ll probably also want to use the Pencil tool to fill in areas with lots of detail or to prevent the Bucket from spreading out too far.)
This process will get rid of shading, changing the image into something more flat and abstract. Here’s a recreation I did of about what the process looks like midway through:

Once you’ve painted everything the color you want, you’re nearly done.
There’s no need to worry about small details with this method. For example, you can see that there are a lot of little dark spots on the roof where the shingles are, but they’ll all get wiped away in the final step when you apply Gimp’s Oilify filter to the whole image.

And that’s pretty much it! I like that the whole process feels kind of mechanical, since that’s central to a lot of Pop Art. It’s not Andy Warhol, but it gets the job done for a game on a tight schedule and (IMO) looks sufficiently different from the preset photo filters to stand out.