Extracting raster values and creating new raster in QGIS?

QGIS has a Raster Calculator that can calculate specific raster bands using mathematical expressions and save that to specific GDAL enabled formats, such as GeoTIFF, Erdas Imagine, etc.
There are a number of additional QGIS plugins as well.
see http://plugins.qgis.org/plugins/tags/raster/ QGIS can be built with GRASS which has raster functionality http://grass.osgeo.org/programming6/gisrasterlib.html

You didn't ask about this, but you might want to consider other remote sensing software such as Optics [FOSS]-- opticks.org

And these industry standard Products of course: Erdas Imagine geospatial.intergraph.com and the exceptional ESRI Raster capabilities. www.Esri.com

Identify Polygons on raster image

This was a similar question. I was looking to take certain parts of the raster out (in my case buildings) and create polygons...but you create a raster first. or create the polygons and then convert to raster.

Load the raster and start the raster calculator. Set an output filename then in the "Raster calculator expression" text box type:

filename@1 = 3

Where "filename" is the name shown under "Raster bands". Then press OK. That's it!

See also: http://spatialgalaxy.net/2012/01/25/using-the-qgis-raster-calculator/

Gdal calc would be another option use

gdal_calc.py -A input.tif --outfile=result.tif --calc="A*(A==3)" --NoDataValue=0

see http://www.gdal.org/gdal_calc.html

If you want to extract the values without having 0's, you need to use a different formula in the Raster Calculator.

"img1@1"/("img1@1">0)

0 values will be returned as no values.