Cooking Shows are an often-overlooked option. Nice in that they are not generally "serials", usually last around 20 minutes without commercials, and show young children not just a wide variety of foods and preparation methods, but also help them understand how what winds up on their plate got there. As everyone knows, the foods on these shows seem to burst with eye-grabbing color, almost impossibly so. Anyway, kids love that!
Gardening Shows, similarly, can be quite good, "low impact" shows, for similar reasons.
During those brief periods of non-wartime, allowing them to see/hear some of what's on the news (in any country besides the United States) can also be a positive experience, especially once they start "axing questions".
As Jameson Quinn said, 1-2 is a bit young for TV in general, but keeping them away from ongoing series as much as possible (except, perhaps, Baby Sign Language instructional videos) is the best way to "trickle in" TV, so that it doesn't become FAR more addictive in later years.
Now that my girl is 3, our regular shows include Doctor Who (TV series) (lots of simpler/pseudo science to discuss, high degrees of creativity and imagination in the plots, and none of the old monsters/effects are very scary to kids these days), Mister Rogers' Neighborhood (some of those topics/themes are pretty dark, but the show was pretty spot-on for pacing, language, and content for the 3-6 set), and Pucca (long story how that started, but with each animated episode lasting only 8 minutes, can be a great "negotiation show" when there isn't enough time before school/lunch/bed).
I think any age below 4-5 is probably too young for solo television/movie watching for children. If they aren't watching with a parent, or at least a couple peers, then the TV watching experience becomes the "dreaded babysitter", rather than a potential conversation starter during or after a given show. With that as your guideline, I suggest the following:
Let your child watch only those shows you would be happy to sit and watch with him/her.
Finally, let me also advise checking in now and then when content may seem too advanced for your child, they start to squirm, or you're concerned it might give them nightmares. If they respond that they're not scared, bored, or otherwise need to be elsewhere (TV can be more interesting sometimes than dry pants, for example), then trust their judgment.
What are the best TV series for 1-2 year olds?