This show was a "modern" adaptation of the popular novel "Swiss Family Robinson", right down to the family name. Most kids of the '60s watched this show - probably because of the action and adventure that included a younger kid, as well as a teen, and 2 young adults. I think that was one of the things that I remember about it the most - watching the trials and tribulations of the "teen" daughter Penny as she slowly "came of age". And interestingly, the "parents" weren't portrayed as "uptight" or "stuffy" as those on other "family-based" shows in any genre of the time (maybe the costumes helped in that respect, as this gave them a more "casual" appearance).
The one person who stands out the most - at least looking back from an adult perspective and recollections of the show's tone from childhood, was the Dr. Smith character. He was obviously a "dark" figure who very much impacted the mood of the show, becoming an overall menace and sometimes nemesis to the rest of the group. But he almost always garnered pity and forgiveness from the family and the viewing audience at the end of an episode, every time his inner coward kicked in and he blubbered his way back onto the ship. I expect whether you like him or hate him, any actor able to invoke an emotional response and make you frustrated at the character's nefarious behavior, means he obviously nailed it. I always cheered on Major West's continual admonishments of Dr. Smith in any case. I guess the other character that was and continues to be a fan favorite (and butt of jokes), was Robot. Some of his dialog survives in the popular culture today, from his now-laughable "Danger Will Robinson!" to his ubiquitous "WARNING WARNING WARNING!", making him a classic and illiciting a chuckle when using any of his phrases in a conversation. As the family watchdog, he performed his role well.
I think all in all, it was a show for its time that attempted to appeal to all audiences and not just the Madison Avenue 18 - 24 age group insisted upon today. And despite the film attempt to remake the show to fit more modern times, the original version still remains a cult favorite that tried to illustrate and underscore that when a family works together, they can stay together, through thick or thin.