First of all, are there any other symptoms? Coughing, idleness.... will he still play or is he sleeping? Second, and most important of all: is he drinking?
If he seems "dopey and lethargic" and he isn't drinking, take him to the vet right away.
Occasionally, cats will stop eating just because they aren't hungry. Is there another cat in the house? Sometimes they'll only eat at night if you leave kibble out for them, and therefore you won't be seeing them eat. Or he might be angry at something having been changed in the house. (That can make them sulk.)
However, it is VERY VERY serious if he is coughing/sneezing or is generally acting sick. (Just sleeping and not interested in anything.)
Another thing to do for a quick check is see if his ears are hot. (And I don't mean "warm", especially if he's been sleeping, I mean hot.) If they are, there's a good chance he has a fever. Also check and see if his third eyelid are out (makes their eyes look funny) and if there is any discharge from the eyes and nose. If his gums are pale (and not a healthy pink) he might be anaemic as well.
It's probably better to take him to the vet, just in case. If it's something really serious, they'll know right off the bat. Cats NEED to eat at least every other day to remain healthy. Dogs can manage without food for up to three or four days without any ill effects. Cats aren't like that though.