Public domain-ness of characters is a touchy situation, because there really isn't much of a concept for copyright of characters. Stories are protected (and can lose protection), which is a little bit easier to manage.
To that end, as far as we've found, no particularly popular franchise/character today has any stories in the public domain that we're spotted. I suspect it's because very few companies would bet the farm on stories that could be adapted by anybody, so anything not protected by copyright would be swept under the carpet. There are minor characters, though.
Eric mentions a few. Many issues by Fawcett, Quality, and Charlton (though the Charlton "Action Heroes" are later than we generally post here--our "competition" across the street goldenagecomics.co.uk veers more in that direction, ironically) weren't renewed. Quite a few characters have also been "borrowed," like Fox's Blue Beetle (who became Charlton's Blue Beetle, then DC's), the Fantom of the Fair (who Roy Thomas used in...I think a Sandman origin), a bunch like Human Meteor (used to fight the Invaders), and so forth. I believe that Amazing Man has made recent appearances in Iron Fist (because he was used as the basis), too.
And, of course, Dynamite Entertainment's "Project: Superpowers" is a fairly popular series that basically takes our inventory and pretends it all happened from 1938-1945, with a modern revival.