As a general rule of thumb when is it appropriate to make a gif interlaced, a png interlaced and a jpeg progressive?
Especially when publishing the image on the web.
JPEG: YES — use progressive scan. It makes files smaller (each pass gets its own Huffman table), and partial rendering looks quite good.
GIF: NO — it's unlikely to make the file smaller, partial rendering is poor, and it's pointless for animGIFs. It's best not to use GIF at all (yes, even for anims).
PNG: NO — it hurts compression (as data from each pass is statistically quite different). If the image is large, use high-quality JPEG or lossy PNG if possible, as these may load quicker than a pixelated preview of a large lossless PNG.
ImageOptim will automatically change progressive/interlaced formats when it makes files smaller.
Disclaimers for nitpickers: