What type of knife befits peeling/skinning melons and squashes?
You're going to be dealing with large, slippery things, with tough skins.

It's really easy to cut yourself with these.

For softer ones - melons - a serrated knife works well in my experience.  A regular bread knife will often be too thin, but a heavier knife with serrations works fine.

For harder items - the fall/winter squashes - I use a shorter-bladed chef's knife or utility knife so that I have more control.