I just stumbled upon this frighteningly adorable Canadian cartoon that just so happens to contain quite a bit of sneezing. The series is essentially described as "perky goth": it's generally happy and upbeat, but pretty much all of the characters and themes are fairly dark and eerie. The story revolves around the titular character Ruby, a weird but always optimistic girl, and her equally wacky friends. One of these friends is a girl fittingly named Misery, and her sole purpose in the show is to have impossibly bad luck and get screwed over all the time. Misery's the one that does the majority of the sneezing, but a few other one-off characters do as well.
Note: The characters' ages are never explicitly stated, but I get the feeling they're not meant to be over 18. Their voice actors were all over 18 at the time the show was initially aired. However, I still don't want to tempt fate so I won't link to any clips unless the staff tells me I can.
All the episodes mentioned here can be found on YouTube, however, so if you really need to find them, you should be able to do it on your own.
- One from Misery about half way through "Once in a Blue Luna" for no reason.
- Several from Misery throughout "A Bad Hare Day" from a cold, one from Doom (the pet cat) about halfway through from being out in the rain, and
several faked by the bunny throughout the first half.
- Several from Misery throughout "The Last Train to Gloomsville" because of an illness that also causes her to exhibit other symptoms such as a fever, and one from the Mystery Man toward the end for the same reason.
I haven't watched too much of the series, so there might be more. These are just the ones I've seen so far.