I think maybe with Charlotte, she's presented as having had a full life and being happy -- it's sad, but not a tragedy. She saved Wilbur's life, and she's part of the cycle of life with her own babies and Wilbur saves her egg sac and the little spiders stay on the farm. Dead dogges (or PONIES, kthnx Steinbeck) always seem like tragedies, and like asakiyume said, kind of practice runs for Dealing with Death but the death is almost never natural. White's books are all about nature, and death is just a part of that, not the ending. And the last line of the book is about her gifts for writing and friendship -- how Wilbur (and the reader!) will remember her.

(I have been arachnaphobic all my days and I still love Charlotte!)