I probably worked 100 or so IOA Character Breakfast shifts (and these, along with the HHNs, were always my favorites), and it suprised me to see the amount of adults who would come in without kids. A rough estimate would be about 25-30 percent overall, which is a fairly large number considering three of the four charcaters (Cat, Thing 1 & 2) are aimed at a toddler set.
Again, this breakfast works on a couple of levels. The character interaction (as has been mentioned multiple times) blows away anything Disney does. None of the pat your head, sign an autograph book, take a pic and they're gone in 30 seconds like Disney does. I've seen Spiderman spend upwards of 15 minutes with kids, and things feed small kids. Seriously, if your kids like any of these characters, this is the best experience they'll have at any theme park.