Are there any realistic pet games to take care of a virtual pets?

Yes, and here's a list of the websites. (see related links at the bottom of the page to get the links to these websites)

• Foopets.com
• MaraPets.com
• Moshimonsters.com
• Neopets.com
• Powerpets.com
• MrFreeFree.com
• Adoptme.com
• Bunnyherolabs.com
• Virtualpuppy.com
• VirtualPets.com