Well, I earned those badges. They are using valuable inventory space... So they do anything important? Or I can just get rid of them somehow? EDIT: My Jackal (belonged to the druid) died and... It had a ring, and badges, and one more other item I forgot. ????
As far as I'm aware, nothing (though I think you can sell them). I usually carry mine round for as long as possible, then stash them in my extraplanar chest.
The badges don't do anything, they are feel-good trophies, nothing more. http://www.co8.org/forum/showthread.php?t=8742 (search "badge")
I sell all but 2, I stash those two in the well in case I ever need them. I never have needed them though.
I use the one of the chests in the Nulb house as a "trophy" case. I put the wooden shield and those badges and so on in there. And maybe a "fireball" or two from the rescued tailor. It also saves space in the (not unlimited) extraplanar chest for carrying loot to sell.
