PNGOut is a free program that optimizes the compression of PNG images. It was developed by Ken Silverman and first released on 2004-04-11, but the latest version was released on 2015-02-13. The program has several options, most of which require a basic understanding of image formats and compression, but the default options will almost always yield better results that a typical graphic program. PNGOut primarily reduces file size by decreasing the color depth to the minimum level possible while still retaining 100% of the color data, and then performing a brute-force check on all compression tables to find the optimum level of compression. Depending on how bad the initial program was at saving PNG images, this can sometimes cut the image size in half, but a file size decrease of around 10-30% is typical.
To use the program with its default settings, simply drag and drop an image onto the pngout.exe file. The free version will only compress a single image at a time, but this is rarely a problem for the average user. A professional version has also been made which features batch processing and a user interface.
I found this program in the mid-2000s while looking through Ken Silverman's website and found it to be invaluable. I use it for all the images I upload to my web site and for large graphic projects I've done.