I'm just wondering if I can use super glue, to fix broken fondant figures?  They're fully dried already, but the head broke off of my elephant.  There are some other parts to this topper too that have broken pieces.  

It should work if they're fully dried. Hot glue might work too, but a low-temp hot glue.

Or royal icing if you want to keep things edible - the thought of glue on a cake scares me....make absolutely sure the recipient knows it's not edible!

You could also join the broken pieces with the same fondant the topper was made from - softened a little with a touch of water to make it more glue-like - it bonds very well if you have sufficient drying time.

What do you mean winniemog?  Like buy some fondant of the same color and bond it with that?  The topper is completely dry, it's solid.  The person I purchased it from, asked me to try adding a little warm water to the head and stick it back on.  It did seem to stick back on, but I'm worried it will fall off again.

Sorry - I assumed you'd made the topper yourself so had the leftover fondant. It's just easier to get a good colour match that way.

You could use royal icing to bond and carefully clean up any excess that's visible before it dries. Good luck.