The relationship between House and Cuddy is, to say the least, incredibly complicated and rife with tension. So many people have accused Cuddy of sleeping with House that even House has jokingly asked if there is anything to the rumor. Some of the audience was left unsure whether they really do have a past, and if their feelings are more than just flirty banter and sizzling hot sexual tension for several seasons. However, House and Cuddy eventually reveal that they have deeper feelings for each other in season five, when House offers Cuddy a kiss of solace in Joy after learning that her planned adoption will not go through. This kiss stirs those old feelings up to the surface.
Their history together is not as clear, but here is what is known for sure. When House was expelled from Johns Hopkins for cheating, he wound up at the University of Michigan. At the same time, Cuddy was attending the school as an undergraduate. House quickly became, as Cuddy describes him, a legend. She pursued him and they slept together one night. The next morning House was notified that he had been expelled. However, the rest of their relationship at this time and over the next twenty years is clouded in mystery.
Fast forward to about five years before the series starts. House is known as the one of the greatest diagnosticians in the world, but is practically unemployable due to his inability to deal with anyone—supervisors, subordinates, staff or patients. Cuddy, on the other hand, has become the second youngest chief of medicine in the history of Princeton-Plainsboro Teaching Hospital. For some reason even Cuddy has kept hidden, possibly in a legal manoeuver to keep PPTH for being sued for malpractice over the way they ignored House's wishes and crippled him, she decides to hire House. Her official explanation is that he came cheap.
However, House has managed to stay at PPTH for some eight years, with Cuddy being his boss throughout. During this time, House has become responsible for half the hospital's legal budget, has continued not only to alienate supervisors, subordinates, staff and patients, but also important donors. He also regularly subjects Cuddy to sexual harassment, commenting constantly on the size of her butt and the display of her breasts. Obviously, no matter how low his salary, it isn't worth the nine figure sum he has cost PPTH. However, when push (literally) comes to shove, Cuddy has always backed House.
Cuddy refuses to discuss why she's never fired House. (Technically she can't, House has tenure and can only be fired by the board acting unanimously, but they despise House more than anyone.) However, when pressed, Cuddy will point out that House has saved about one patient a week. She also realizes that House is a much better doctor than she is.
At the end of the episode Top Secret, there were additional but non-explicit clues. House remembers where he had seen the patient before - making out with Cuddy at a hospital fundraiser. Cuddy says the only reason why House had remembered him (he never remembers anyone) is because he was making out with Cuddy. She intimates House wanted her himself (she made the same observation in Insensitive). House says that Cuddy hired him because, for one night, he gave her everything she asked for. She tells him not to fool himself - he couldn't get hired anywhere and she picked him up cheap. She tells him to get over her.
However, in the previous episode, Insensitive, Cuddy's blind date left her because, although he liked her, he noticed how much more excited she was when she was around House.
The recent events surrounding Eric Foreman's employment have given some insights into Cuddy's motivations. We can guess that although House has been fired several times, he may have, like Foreman, have been fired for saving the life of a patient at the expense of his job. We also know that Cuddy continued to defend House even though Foreman pointed out that if every doctor acted like House, the mortality rate among patients would skyrocket. Cuddy appears to have both the necessary tolerance for House's methods (which do, after all, save lives) and the willingness to stand up for House when everyone attacks him. We can surmise that Cuddy hired House in much the same circumstances that she re-hired Foreman, and perhaps for the same reason - to teach them both a little humility and get an excellent doctor in exchange.
It is also possible that Cuddy's motives for keeping House around are a mirror image of House's reasons for tormenting Cuddy. House gets some unhealthy satisfaction out of evading or defying Cuddy's rules, and Cuddy seems to get the same satisfaction out of successfully imposing those rules on House.
In Season 4, at least as early as the episode "Mirror Mirror", Cuddy is taking birth control pills, of which, strangely, House is aware. He further suggests that he switches the pills as a prank. During a conversation with Foreman, he quips that if Foreman stays: "No one's going to be happy here... and Cuddy's going to end up pregnant." Foreman, caught off guard by the comment, quickly asks House: "Are you saying... What does you having sex with-", but House immediately deflects the question. Evidently, it could suggest House has feelings for Cuddy.
Lucas Douglas, who likes Cuddy himself, certainly thinks House is romantically interested in Cuddy, as he saw no other reason for House's attempt to get Cuddy to reveal something about herself to Lucas. House's official explanation was that he was looking for leverage in negotiations, but Lucas rejected that explanation.
When Cuddy decided to adopt a child in Joy and House was desperate to prove to her she wasn't ready, Wilson realized that House's attempts to keep Cuddy childless were merely a clash between House not being willing to admit his attraction to Cuddy and his fear that Cuddy's interest in becoming more of an adult would create a permanent rift between her and the still adolescent acting House. When Cuddy snapped at House after he reversed course and said she would have made a great mom, he suddenly kissed her.
House and Cuddy both admit their feelings for one another in the episode Under My Skin, where Cuddy says she only took the Endocrinology class she shared with House because she "thought he was an interesting lunatic, even then." When Cuddy goes to leave, House thanks her for helping him get through Vicodin withdrawal, and Cuddy asks him if he wants to kiss her. House replies, "I always want to kiss you," and the two share a quick kiss. After a second, they begin kissing passionately as the episode comes to a close.
Of course, as of "Both Sides Now", it revealed that Cuddy never helped House wean himself of Vicodin, and that he simply hallucinated from the Vicodin. Thus, we can disclaim the previous paragraph.
Throughout season 6, House has attempted to prove to Cuddy that he is changed and capable of a serious relationship. For the earliest parts of the season she flirts with House, but then for the rest she pushes him away because she is in a relationship with Lucas Douglas (though it's never clear when that began), and in the season six finale, "Help Me", she tells House that she has left Lucas, whose proposal she'd accepted the day before, and that she loves House. Afterwards, she and House kiss.
After a tumultuous stab at a mature relationship in Season 7, Cuddy dumps House after a cancer scare which House cannot bring himself to confront without the aid of his old friend Vicodin. Cuddy realizes that House is not and probably never will be ready for a real relationship and ends it. House attempts to convince himself (and everyone else) that he is over Cuddy via his usual juvenile methods, but the flimsiness of his carefully constructed house of cards (pun intended) is revealed in Moving On, when House's Dodge and Cuddy's dining room pay the ultimate price while revealing House's self-deception. Based on Cuddy's assertion that she wants House arrested if he ever comes near her again after this incident, it may be safely assumed that the final nail has been driven into the lid of the Huddy coffin.
(Should have been 'Hou-ddy', sounding like 'Howdy'.)
See also Huddy Links