Lilo & Stitch / Leela & Nibbler
Lilo & Stitch came out in 2001, depicting an apparently male alien creature who is incredibly destructive and dangerous in spite of how cute he looks. The creature is adopted as a pet by a girl whose name is two syllables long and uses the letter "L" twice. After making only cute noises through the first half of the movie, Stitch eventually reveals that he can talk and he occasionally says smart things. He plunges the protagonist into danger.

Nibbler's first appearance on Futurama came in the fourth episode, which aired in North America on April 13, 1999. Nibbler is an apparently male alien creature who is incredibly destructive and dangerous in spite of how cute he looks. He is adopted as a pet by a girl whose name is two syllables long and uses the letter "L" twice (Leela). After making only cute noises through the his initial appearances in the series, Nibbler eventually reveals that he can talk and he occasionally says smart things. (At least as smart as the other characters, which is not a very high bar to vault over.) He plunges the protagonist into danger.

I'm not the first person to point out the possible rip-off, but I am probably the saddest.

* Actually Nibbler first appeared as a shadow in the pilot episode, but this is not clarified until much later.