Penny (Kaley Cuoco) on "The Big Bang Theory" is the only main character that does not fit into the nerd subculture, although she has began to show more interest in intellectual subjects over the past several seasons. Her last name on the show is also unknown which is another way that she is separated from the rest of the main cast.
Penny has had important interactions with all four male characters to different degrees. Penny and Leonard (Johnny Galecki) had an on and off again relationship over the years, a plot arc which has lasted since the very first episode when Leonard began to develop feelings for Penny. After their relationship ended they attempted to continue a friendship although the success of this varies depending on the episode. Penny herself has confirmed that she still harbors feelings for Leonard since their break up. Penny and Sheldon (Jim Parsons), despite not being romantic, may actually have the closest bond and the most screen time together. A large part of this can be attributed to the growth of importance in Sheldon's character, who was originally intended to be less important but quickly grew to be the breakout hit. Penny and Sheldon's relationship is purely platonic and almost brother sister like. The friendship started around the time Sheldon became sick and Penny had to take care of him, culminating in the "Soft Kitty, Warm Kitty" song which was a song that Sheldon's family sang to him to make him feel better.
Penny also has interactions with Howard (Simon Helberg) and Raj (Kunal Nayyar), although to a lesser extent. It is clear that she considers them as part of her circle now, but at the beginning she did not have much to say about Raj and was actively repulsed by Howard. Raj was unable to speak to her without drinking alcohol due to his problems with talking to women and Howard was always trying to get her to go to bed with him.
Penny's personality initially appears to be the typical shallow girl focused only on vanity, but as time has passed and her relationships have grown, she has shown that she has a great sense of humor, is capable of caring for others, and has a good sense of self. Penny, before dating Leonard, went through many relationships and Sheldon has predicted that she has slept with about 30 men a figure Penny denies. After dating Leonard, Penny tried to date some of the "hot but dumb" guys that she used to like but admitted that after being with someone with substance it is difficult to return to that type of relationship.
"Holy crap on a cracker!"
"You don't have to thank me every time we have sex, sweetie."
"Anybody want to buy a pair of my panties for $1,400?"
"No, I don't wanna try it! My God, you are grown men! How could you waste your lives with these stupid toys and costumes, and comic books, and-and... now that-that..."