Back in the day when I was a lot more of a social hermit than I am now, I never took part in (or even cared about) the community. The things that made me attracted to virtual pet games were their:
Accessibility
Pets (from their graphics to their written description)
Pets I would make characters out of (because I still used to do this, I now dislike hoarding virtual pets-- unless it's pokemon-esque games)
Story (if they have any)
And there was always a thrill I got from progressing a virtual pet game with a pet I've grown with and have given value to... Like one of the first VP games I really loved was this site called PowerPets (it's still alive, but it's pretty much barren, everything is now outdated and the newest layout is horrendous). But on that site, there were a lot of things I could do on this site that made me feel like success came from the individual (like a single pet getting stronger or you progressing through a story) rather than how much you have (like -of course- wealth and pet hoarding). I have since adapted to the more social aspects of virtual pet games, and while it's nice to have big, lively communities in these browser games, that should not always be the main reason of a game's greatness.