I have never felt emotional about the absence of dinosaurs from the world. They lived so long ago, and seem so alien.
But I occasionally get misty eyed about animals that disappeared within the past few thousand years -- in geological terms I came so close to seeing them. Just 13,000 years ago dozens of now vanished species of large mammals roamed the Americas. Imagine a world with dire wolves, cave bears, sabertoothed cats, mammoths, mastodons, giant ground sloths -- all gone. Pigmy mammoths survived even longer, until 5000 years ago. That marsupial ground sloth above, Parchestes azael, was another strange animal the lived long enough for people to know it well and depict it in rock art. I mourn these losses, sometimes, and I delight in thinking that we might be able to bring some of these vanished creatures back.