Multiple Futurama episodes got tears out of me. I think it's a normal and natural thing to be touched by a piece of media to the point of tears. I've watched them again in fact.

Once per season they had the tear-jerker episode.

"Luck of the Fryish" has always been a favorite of mine. Not quite as tear-jerking as Jurassic Bark, but still a little sad with a somewhat somber ending.

Of the tear-jerker episodes, I really like "The Late Phillip J Fry". Most people tend to take it into account in the series continuity.

It’s really weird that people seem more emotionally affected to the episode about the dog than the ones about Frys family...

People frequently show more affection in movies to animals than to humans. The Walking Dead spent years graphically and brutally killing humans both dead and undead and no one flinched. Then one episode the starving protagonists killed a pack of feral dogs for food and suddenly there were tears shed.

Luck of the Fryish... if that's the one with the Simple Minds song, it definitely affected me!

Don't you forget about me...

Yep! It's the one where Fry remembers the seven-leaf-clover. I thought the scene with Yancy naming his son Phillip since his brother went missing was one of the best scenes in the series.

That's my favorite episode, personally!

Just hearing the song that closed that episode makes me want to cry.