Always screen videos before showing your kids.
French
TFou offers many cartoons and activities for preschoolers including Dora the Explorer, Chuggington, Franklin, Babar and Olivia.
http://www.tfou.fr/
Spanish
RTVE offers a wide variety of children's cartoons that include simple vocabulary and phrases in Spanish. Some of the ones I found are Caillou, Arthur, Spongebob, Clifford, Dora the Explorer and many more.
http://www.rtve.es/alacarta/programas/tve/infantiles/1/?emissionFilter=all
Italian
RAI (Radio Televisione Italiano) offers a wide variety of children's cartoons that include simple vocabulary and phrases in Italian. Some that I found are La Pimpa, Mickey Mouse Club, Pororo, and L'Albero Azzurro (a show similar to Sesame Street).
RAI also includes "Lo Zecchino D'oro", a show which features simple and catchy songs sang by children.
http://www.rai.tv/dl/RaiTV/cerca_tematiche.html?Junior
Cartoonito offers cartoons, activities and printables aimed at preschoolers. Cartoons include Caillou and Looney Toons.
http://www.cartoonito.it
German
Tivi offers cartoons for all age ranges along with activities and games.
http://www.tivi.de/
Russian
This blog features video clips from some Russian classic films such as "The Adventures of Buratino" and "Adventure Electronics".
http://clipmovies.blogspot.com/
The eye of the child offers simple cartoons for children. The Russian track is recorded over the English track. I found it annoying at first, but got used to it.
http://wwitv.com/tv_channels/b4974.htm
All Languages
BookBox is a website that offers videos featuring storybooks with subtitles. It includes stories in more than 20 languages.
http://www.bookbox.com/index.php?pid=95
Viki offers entire episodes of popular foreign TV shows in 20+ languages.
http://www.viki.com/channels?category=tv