Guilt is often a powerful motivator for heroic types. Batman, Spiderman, even Severus Snape. And Klaus Wulfenbach. Klaus is unwavering both in his devotion to his son's safety and to keeping the peace of Europa, and he doesn't go about it lightly. He works with a heavy heart, taking no joy in his successes, accepting no praise or titles or accolades (as far as we know). Klaus has apparently never had an interest in being recognized as a hero. He almost seems to shun these things. Deep-seated guilt is just one possible explanation for his character, but it seems the most likely. There are several possibilities for the source of his conflict.
The Secret Blueprints tell a story about an accident involving three sparky Wulfenbach brothers but only one survivor. What most fans "know" is that Klaus was killed at some point, then later resurrected and reassembled with spare parts, presumably from his two deceased brothers. Whether his reassembly was completed by his parents (a theory I favor) or the Heterodyne Boys doesn't matter: the end result is the same. Klaus now carries a constant physical reminder of his siblings and that accident.
Survivor's guilt would be enough of an explanation for his attitude, but Klaus isn't merely sad -- he's angry -- and much of that anger seems to be directed inward. What if a young, carefree Klaus, by arrogance or recklessness, caused that accident that cost his brothers their lives? Every single time he looked at the hand that wasn't always his, the limb that used to belong to someone he loved, he would be reminded of that mistake and the price that was paid.
Bill and Lucrezia
Klaus undoubtedly carries some guilt about his affair with Lucrezia. Bill was his friend. Whatever he had with Lucrezia was meaningless compared to the friendship and loyalty he felt to Bill. His reaction is pure offense and outrage (and, admittedly, possibly a little jealousy, which would also weirdly compound his guilt) at the suggestion that she's going to take advantage of Bill. It's quite likely that Lucrezia seduced Klaus merely to drive a wedge between the two friends, knowing that their friendship would have to be destroyed in order for her plan to work.
So not only must Klaus have been experiencing guilt at the time he carried on the affair, he must be facing even more over his role in everything that followed because of his actions. If he'd kept his head about her, he might have been in a position to stop Bill from marrying her (or so Klaus thinks).
The Lost Years
Lastly, Klaus was gone for a few years as a result of Lucrezia's interference (which he may also see as his fault, for reasons outlined above). Whether it was his choice to remain gone or not, it's likely he may blame himself for what happened in his absence. If he had only been there when Lucrezia (The Other) attacked.... If he had only been there to warn Bill, or fight alongside his friends.... His personal horror would only be compounded if it was his choice to remain gone.
This is also possibly the real reason for his furious hatred of Lucrezia -- he's not mad at her, he's mad at himself. In his view, he should have seen this coming and could have prevented it all.
Klaus certainly doesn't dwell on his guilt. It's not something he thinks about -- it's under the surface. He can't afford to be distracted or allow himself the luxury of wallowing. While his guilt doesn't manifest on the surface, and Klaus is adept at distancing himself from his emotions, it clearly must play a large role in his motivations. It should be no wonder that he denies himself things that make him happy (his wife, his lab) in pursuit of his very noble goals.