The Curious George cartoon is great–funny and educational about math, science, and social studies.
It has a very ethnically diverse group of characters. If you’re looking for stereotypes, see an episode with “Chef Pisghetti”, the Italian chef.
One thing I find puzzling is that Bill, a very intelligent, African-American boy who looks about twelve, keeps referring to George as a “city kid”, and in several episodes it’s made clear that he thinks George is human.
Sesame St will probably be the best one for your essay, because it’s been going so long and is so socially aware that it will be very easy to answer the questions on your list and add extra info, like how it’s changed since the seventies or how different versions around the world vary from the US version (the South African version has a character with AIDS, for example). It’s a piece of social history in itself.
My 2 year olds favorite shows are Max and Ruby, The Cat in the Hat, and Toopy and Binoo.
Out of those three The Cat in the Hat does not make me want to rip my eyes out.
A couple my kiddo likes that others haven’t mentioned: Oswald, Olivia, Peep and the Big Wide World. I really like Peep, because it’s low-key, teaches some good science-y concepts, and Quack cracks me up.
Teletubbies, if your young children are dabbling in recreational pharmaceuticals. 
At least you ought to get some interesting gender-role stuff out of it, since the lead male character (Tinky-Winky) proudly carries a red purse.
Wait—is that the purple one? You mean he/she/it really IS gay? 
Nope, Tinky’s not gay (or at least nobody knows for sure). He’s a young child. Some young boys like to carry purses. The whole “gay” thing was started by Jerry Falwell and that bunch.
My nearly 2-year-old LOVES the Wiggles. It’s Australian, but it’s also the most tolerable show for children I’ve seen.
Well, this thing is due on Wednesday, so I’ve spent the entire day watching children’s TV. So far I’ve slogged through Mickey Mouse Clubhouse, Thomas & Friends, Chuggingtons, and Max and Ruby. The only one I like is Max and Ruby. Sure, Ruby’s a snotty little bitch and Max is clearly a high-functioning autistic, but the animation is pleasing to look at, and it doesn’t have the same in-your-face frenetic inanity that most of the other crap I’ve watched seems compelled to bombard you with. I seriously thought that the Mickey Mouse Club was going to trigger a gran mal seizure. Tomorrow I’m going to check out the Backyardigans, then hammer out the final report.
Hah! if you think that is chemically enhanced you should try another one from the same stable.
It has Sir Derek Jacobi narrating and it is hypnotic. My little ones loved it around the ages of 2-3. It was designed as a “wind-down” before bedtime.
Actually, you might consider that aspect in your assignment. How different shows fulfill their different remits. Here is the BBC site that explains a lot of what they do but I’m not sure if you’ll be able to see the clips (region restrictions)
I’m glad that you like it, it’s one of my preferred selections for my son. It’s nicely paced, has cool music, and I like the interplay between the two. I also think the toys are a hoot.
If you have time to catch Dora, you can also comment on how her parents refuse to get her a shirt that fits.
My Little Pony: Friendship is Magic is pretty awesome no matter what age you are. All the episodes are available on youtube.
I freakin’ LOVE the Backyardigans! Mission to Mars—the Mars Rover barks like a dog and plays fetch. Rover—get it? BWAAAHAHAHAHAHA!
Backyardigans are teh awesome. I think my wife and I like it more than the kids. I particularly love how the music follows a theme each episode but the musical theme sometimes has nothing to do with the plot. Big band swing singing Medieval Knights? sweet…
Does it have to be current? Find an episode of You Can’t Do That On Television, it’ll give you lots to write about.
Actually, it’s done. I just finished about five minutes ago. The final paragraph needs some refinement, but other than that I’m satisfied with the outcome and am pretty much going to leave it as is. Does anybody want to [del]ridicule and bash[/del] critique it? It’s less than 1000 words.