It's a bit of an explanation, but I'll go through it all.

You need a copy of Photoshop or another program that can stitch images together (Photoshop has an automated process for it). You also need to be a little handy with image editing.

For Mirror's Edge and Unreal Engine 3 games, there's two commands that are important for this. One is "tiledshot", which takes a screenshot that's much larger than your resolution. I take screenshots at four times my in-game resolution.

The second command is "FreeFlightCamera", which lets you toggle the camera to a few different views. One of them is a free-floating camera, like no-clip but leaving the body behind. For Mirror's Edge, I had to find a spot where there was nobody chasing after me, then from there I would use the FreeFlightCamera to move to where I wanted the panorama.

From there, don't move the camera except for turning it. It's exactly how you would take a panorama with a photo camera, one picture every 15 degrees or so (about 24 pictures). I'd then angle up a bit and take about 6-8 screenshots, then angle down and do 6-8 more. From there, you can stitch them all together, find a common seam, and edit or blend it until it appears seamless. Then, crop!

I know it's not the best explanation. ^^; Source engine games are similar, use noclip and set it up where enemies can't see you, then find an area that you want to take screenshots. Both Source and Unreal Engine allow you to disable the HUD, too, which is important.