I would like to have a Stack Overflow icon similar to the icons I have at the top of my site. Does Stack Overflow/Stack Exchange provide free icons or what would be an alternative to getting an icon on my site?
If you're talking about the SO logo, you can find a higher resolution and vector version here: http://stackexchange.com/about/logos
If you want a high resolution logo for every site then there is another way that results in high resolution, raster graphics.
Basically, all the site-specific icons are a deviation of the following URL.
Just replace the name stackexchange with the name of the particular site you want to use. Tada! You now have a nice, high resolution icon. Take the following examples.
NOTE For meta sites you have to append meta to the main site name. For example, the icon for Stack Overflow Meta would be...