They're not human, but pets are part of the family. We grieve when we lose them. I had a Betta several years ago named Fred. I wept when he died.
I hate to bring the thread down, but here's something some may find interesting:
I'm not saying I have The Shining or something like that, but when my brother passed, I woke up from a deep sleep and knew he was gone. In fact the time they put on his death certificate was 3:15am. I woke up at 3:13am.
Several years ago, my girlfriend at the time bought a Bernese Mountain Dog, Digby. He and I got really really close. So close that after she and I broke up, she would still invite me to come visit to spend time with him. It's an arrangement that my most recent ex and I have with our two cats, Cupcake and Sushi.
Anyway, I was at the Art Museum here in Houston one day. On Thursdays it is free, so I will sometimes go if I have a doctor's appointment as the museum district is right next to the medical center. Well, I was in the Asian section and was looking at a statue of The Buddha. I am not particularly religious, but for some reason that statue moved me tremendously. So much so that I started crying, and couldn't stop. I actually had to leave the museum. Well, the next day I got an email from Lisa (my ex) and she told me that Digby had died the previous day. Turns out that the time he died was around the same exact time I started crying in the museum. Now, I wouldn't come to me for lottery numbers or anything, but it shows the emotional and sometimes ethereal connection we form with our pets.