On Russian State Television, they still have the program "Good night, children". It's a long-running kids' show shown before they go to bed, with human and puppet hosts (the little bunny and dog are the favorites). They also show lots of cartoons. The American "Tom & Jerry" is shown a lot, but they also show Soviet cartoons. (No cartoons worth mentioning, if any even, are made in post-Soviet Russia. But the best ones have already been made, anyway!)
Also on the network is "Help Telek", and he'll show you cartoons, too. It's a guy (guy character, used to be played by a woman, now it's a man actor) dressed like a television, and you're supposed to help him on his way.
None of the other networks have as good childrens' programming as Russian State Television. In the USSR, there were a lot of good programs for kids, like "A-B-V-G-Deka" (the first 5 letters of Russian alphabet), which taught the language, and had a lot of fun things for kids to experience.
Unfortunately, probably 90% (I'M NOT KIDDING!) of childrens' television in Russia today is imported from the U.S. or maybe England. NO ONE likes it, people are always writing into newspapers to complain. But no one in Russia wants the expense of making their own programs anymore. So kids learn NOTHING about Russian culture, just what they do abroad.