Take a psd and export all the layers into separate image files without using Photoshop

There is a tool from Telegraphics called PSDParse that should do the trick.

psd2png.exe -w Filename.psd

usage: psd2png.exe [options] psdfile...
-h, --help show this help
-v, --verbose print more information
-q, --quiet work silently
-w, --writepng write PNG files of each raster layer (and merged composite)
-d, --pngdir dir put PNGs in directory (implies --writepng)
-m, --makedirs create subdirectory for PNG if layer name contains \'s
-l, --list write an 'asset list' of layer sizes and positions
-s, --split write each composite channel to individual (grey scale) PNG

Here's a link to the version I used, or you can go to the website for the latest version for your operating system.

http://www.telegraphics.com.au/sw/files/psdparse-1.7b1-win.zip

If you don't want to install any plugin, do this using GIMP (open source tool):

1. Select the layer and copy Ctrl+C or Edit > Copy
2. Then Select > File > Create > From Clipboard, this creates a new document from the copied layer, or you can just make the layer you want the only thing visible.
3. Then select > File > Save As... then go down to "Select File Type (By Extension)"
4. In the box where it says "All images select that box and go down to "PNG image (*.png)"

There's a plugin for that: Export Layers as PNG.

It adds an entry to the File menu, Export layers -> as png.