a new game

You mean Simeon (BeBop)??
http://catoftheday.com/archive/2002/June/05.jpg

Yes, I love his face.
Your turn

She's a dog, but wasn't "Dog of the Day".
She's a JRT from my state.
Name starts with S, ends with Y.

Go to Cat/Dog/Pet of the Day Search and search for dogs and type in Jack Russell Terrier. Should find her in the list of JRTs.

Ok I found it using your clues, I just expected a dog to be Dog of the Day and not Pet of the Day but I see that it is an older one when there was just Pet of the Day and not Dog or Cat of the Day.
Anyway, I think it must be Sassy!
http://petoftheday.com/archive/1997/September/28.jpg

You didn't want it too simple, did you??:D :D

Here is the next one

1)This horse was Pet of the Day early in 2002.
2)He does tricks, likes dogs and wears a hat.
3)His name starts with an S.