Sure, the children resemble small valises, but we get tons of comments on every trip from admiring fellow travelers. I am, in fact, surprised that more parents of young children don't affix some sort of ID onto their kids.
If you want something more polished than a luggage tag, there are several online options for kids ID bracelets.
My Precious Kid. My neighbor just ordered one for her daughter for an upcoming trip to Martha's Vineyard (lucky!) and it looks sturdy and cute.
Petite Baubles Boutique. They offer slightly more upscale (and spensy) bracelets in stainless steel, gold filled, beaded or sports bands.
Lovable Labels. Medical IDs as well as regular IDs with straps that look like they'll stay put.
Even a piece of paper pinned to their shirt (ala notes-home-from-teacher-circa 1975) will ensure your contactability if you become separated from your child.