Invader Zim is a very strange show indeed. And it is this strangeness that is precisely the problem with the cartoon that many would consider one of Jhonen Vasquez's magnum opi (opuses?). In every episode, weird, morbid things happen. Zim harvests organs from other classmates. Dib turns into a bologna. Gaz is put under a spell that prevents her from tasting anything but pork. Schoolchildren are almost sent on a one-way trip to a room with a moose, thanks to Zim's machinations. Things get very odd very quickly.
While many enjoy this show and find it hilarious, others, such as this reviewer, consider the bizarre, creepy atmosphere of the show oppressive and nightmarish. Sensitive folk would do well to avoid this prime example of horror-comedy, but those who are more accustomed to gruesome gallows humor and gross goings-on will be more likely to enjoy this show. I myself dislike the cartoon as a whole for its creepy stories and its rather mean-spirited atmosphere ("I will be calling all your parents and telling them to love you less", anyone?), but I enjoy the characters and the ludicrous dialogue, and find myself snickering at it occasionally.
So, give the show a try, but if you feel it's too creepy, weird, or upsetting for you to watch, I recommend you watch another show. Additionally, really young kids might not want to watch this either- they're impressionable and will probably end up having nightmares.