In "The Big Bang Theory" Season 7 Episode 12, "The Hesitation Ramification," Penny got down on her knee and proposed to Leonard. It was an impromptu marriage proposal and Leonard was not prepared for it. He hesitated and did not say yes, which made Penny take the marriage offer off the table.
[Youtube/The Big Bang Theory]
The marriage proposal came after Penny's three-line role in NCIS got edited out. Leonard's attempt to cheer-her up infuriated Penny more. In the marriage proposal clip, one can see a sloshed and dishevelled Penny coming to the apartment of Leonard. She is there to apologise to Leonard for her unreasonable behaviour.
Penny can be seen telling Leonard that she was just upset with herself, and was not mad at him. She feels that everything is falling apart and complains about her temporary job as a waitress that she is ever doing it. She cannot quit her waitress because she cannot do anything else. She sees her role in NCIS as a big break, which also has gone away and that is making her frustrated.
Leonard tries to pep-talk, telling her it is just a minor set-back. Penny does see it the same way, as she has been there for ten years trying to make it as an actress and there is nothing to show for it.
Leonard says: "You've me." This one brief soothing line makes Penny propose to Leonard. Penny holds his shoulder and says, "You're right, I do have you. Let's get married."
Leonard is stumped and just says: "What" Penny gets down on her knee and properly proposes to Leonard. She asks, "Leonard Hofstadter, will you marry me?"
Leonard has a stupefied expression and one can hear him saying: "ah hmmm." Leonard feels that Penny is sad, drunk and feeling lost, that may have made her to propose. Penny storms-off the apartment, and later Sheldon asks a sleepless and sad Leonard whether his relationship with Penny is over. Leonard is not sure about that.
Penny and Leonard have come a long way in their relationship. It is highly unlikely that they will break-up, but the proposal might make them think seriously about the next step.