Well, I'll come out and say it proudly. Gary's wrong here.
If you're going for an epic, serious tone, then keep comedy to a minimum. You wouldn't want a villain named Poofypants, or at least not an archvillain, but having a henchman or a side character who can be the butt of the party's jokes is actually kinda useful. Indeed, if the players in your group are the kind who want a fun game moreso than an epic game, comedy relief is a must. Being all somber and serious all the time ain't fun, and can lead to dissension in the ranks.
For instance, in my game back home, I had myself and one friend who were Role-Players with capital RP, and then three casual gamers who did it because it was fun and because we got to hang out. I originally tried to be serious and epic, but they weren't really the type to get too deeply or emotionally into character (high school guys, ego problems, go fig'). One of the villains of my first story arc was named Limoges. To my horror, when they heard his name, they started referring to him as "Lemon Cheese." The villain I had wanted to intimidate my party, to be the bane of their existence, was now just kinda cheesy.
To my chagrin, this happened several more times with other NPCs, making my game a bit more like fantasy-comedy than fantasy-drama. I had to spend most of my time idiot-proofing my villains' names so they couldn't be mocked so readily.
Then, finally, I shrugged, and decided, hey, they're having fun regardless of whether I make it wholly serious. In fact, when I try to be too serious, they get a little uncomfortable. I should just go with the flow and have a game that is fun for their sake.
Thus, when I was planning my next game, I decided to give the villain some henchmen to be whipping boys. The main villain was a patron of the arts, so his trusted servants were all bards. A group of bards, in fact. A group of bards that sing a capella and go by the name of "Aural Pleasure." It worked pretty well, in my opinion. Because they were able to get their whackiness out of the way with the henchmen, the climax of the game managed to be quite dramatic.
So, in my opinion, a healthy dose of humor is important in keeping the game fun. Even in tragedies like Macbeth, Shakespeare would usually start with a comic beginning to lure the audience in, and then craft the tale so that those who just came for entertainment can be satiated early. Once their desires for comedy are fulfilled, they'll often sit back and be more willing to accept the rest of the story, even if it's not quite as humorous.