In the later Fox seasons, Klaus was shown to be the smartest and most reasonable character in the family, often trying to warn or advise the Smiths of their wrongdoings of selfishness, stupidity, or recklessness.
But this slowly changed as the series progressed, and in later seasons Klaus is shown to be much more prone to being crazed and senseless and (when they listen to him) even encourages the family's amoral and obnoxious actions and behavior.
Klaus does things to get Roger into trouble for his amusement, like when he tricked him into eating Francine's potato salad in "Deacon Stan, Jesus Man".
Among everyone else living in the Smith household, Klaus is very much the most aware and sensible of Roger's contemptuous, abusive, and insanely-vindictive nature of selfishness and lack of morality and occasionally tries to warn the rest of the family against listening to or getting involved with him.
Such instances, however, are ignored by everyone's naivety and general inability (or lack of interest) to take most matters seriously or remember that Klaus is a "man in a fish's body" rather than just a mere talking goldfish, as said in "Dr. Klaustus".
Although Roger has claimed to hate Klaus in the past, they do have a bond and are capable of being civil to each other such as when they head to Europe together in "Red October Sky".
Further evidence of this can be seen in "Pulling Double Booty", as Roger and Klaus are quite content to watch a movie together and show annoyance when they must pause it as Stan intrudes with the cookie dough.
Stan's refusal to help Klaus find a human body, as well as his tendency to treat him with marked disrespect, is often a source of tension in the two's relationship.
The two have become closer in recent episodes, doing activities together such as hosting a podcast about 90s' music and stopping street crime when Klaus inserts his mind into Stan's car.