What do rare penguins do on Club Penguin?

Answer 1

Rare penguins on Club Penguin probably visit it only a few times in a year, mostly to just check what's going on, or to collect new items.

A rare penguin accounts are often traded or given for free, therefore, the new owner of the account will usually show-off his account and enjoy it as much as he can (which, after he has enough of it, will result in passing the account on to another person).