Every anime has it's funny, even hilarious moments. But not many are built around these moments. Gintama, for the most part definitely is.
This anime is completely insane. It's full of random hilarity and antics, while still maintaining a storyline (per episode and arcs). You don't even have to worry about fillers, because you won't know when they hit you, as there is no general plot. Plus, the fillers are just as funny and awesome as the other episodes, if not more. There are tons of references to anime and Japanese culture, which is kind of a down side for a person who isn't familiar with either or both. This reason also makes this anime almost impossible to dub and very hard to even sub! However, if you do get the jokes (and not all of them are reference related), you'll be in tears. It's not all just laughter though. There are definitely some heart touching, throat lump forming, beautiful moments in the anime too (though not as much).
All I can say is, if you're an anime fan and haven't watched it, you're doing yourself a big crime by missing this one. As the title says, I not only class this as one of the greatest anime, or even one of the greatest TV shows, but one of the most brilliant pieces of entertainment mankind has ever created.