Even pets like to feel nice and clean. But they can’t hold a sponge or toothbrush, so they need your help. This game lets a young child work step by step through the process of washing, drying, brushing, clipping and accessorizing one of several cats or dogs. The actions required are very simple and a child as young as 3 could probably have fun with this with a little help getting started.

Rinsing rover with a mouse controled floating shower head
The screen can be resized and audio can be muted as you may prefer. When finished you can view and print a picture and play as many times as wanted. The game is totally free. It seems to be available on several sites, most of which require viewing a 15 second to 30 second ad before the game will launch.
Judging by the ratings and comments of those who played the game, it is quite popular with the younger set, especially girls, but very young boys would have fun with it too.

Brushing a freshly scrubbed pooch
Here are some places to find it:
http://www.girlsgogames.com/game/pet_grooming_studio.html
How to Play:
To use the sponge, shower head, towel, blow dryer, brush, and toothbrush: click and hold the mouse, then move it quickly back and forth over the pet. To use the claw clippers, click over each claw. You can also accessorize your pet and take pictures of him or her when you are finished.

Fun choosing accessories
For a game for a slightly older audience try Devilish Pet Salon.