Much like Ghost's Anime Kitties, Pocket Bishonen were a common sight on early 00s anime fandom pages. Pocket Bishonen was a parody of Pokemon / Pocket Monsters - but instead of capturing small creatures, you would capture male anime characters ('bishonen' meaning a beautiful boy in Japanese). The idea was that you would take a quiz to prove that you knew the character well, and this would allow you to 'capture' a bishonen (save the adoption image). Longer quizzes allowed you to receive badges from gym leaders.
While the old website is long gone, fans of the original have taken up the the domain and revamped the site with new bishonen and badges to collect. There was also a sister site called Pocket Bishoujo, which focused on female anime characters. I have added my personal collection at the bottom of the page.