I remember our dog dying.

I was 12, she was 13. So she had been with us my whole life... she died of cancer.
We had a choice to either put her on a diet and stuff (but that would have been painful), or to let her pass away. We chose for the latter, so she died before my eyes. I cried.
Like TML, I didn't like the idea of getting a new dog (or with other passed away animals) because I didn't think it could replace the other one. And that's still my opinion although I've never tried it.
My pony is getting kinda old (almost 16) and like Germy, I'm also trying to prepare myself for her death.

Problem is that ponies can get a lot older than that... So it could happen next week, could happen in 10 years.