Absent-Minded Professor: Fits the stereotype perfectly, though he's not quite as absent-minded as some. In fact, more of the problems that come from interacting with him tend to be Lamarr's fault, rather than his.
Admiring the Abomination: He's implied to be the scientist who finds headcrabs fascinating in the first game, leading to him keeping one as a pet in the second.
Ambiguously Jewish: Has a Hebrew given name (though admittedly, Hebrew given names are nothing of an oddity in Europe) and a German surname, and named his pet headcrab after a Jewish actress.
Ascended Extra: Like Barney, he's a stock scientist from the original game turned into a main character in the sequel.
Crouching Moron, Hidden Badass: The badass is hidden pretty deep down, but, he did manage to escape from Black Mesa alive and stay alive for years afterwards as a rebel. There are a few subtle demonstrations of this competence:
Despite struggling to keep Lamarr out of trouble, there's something to be said about how he managed to catch a headcrab alive and surgically remove its zombifying fangs without getting turned into a zombie himself.
When Gordon and Alyx teleport from Nova Prospekt right outside Kleiner's lab, Kleiner greets them with a shotgun, clearly not expecting them and very ready to blow away any Combine intruders. Thankfully, he instantly eases up when he realizes who has just returned. Additionally, inside the lab, Gordon can find the wreckage of a Manhack, most definitely destroyed by Kleiner himself.
Fluffy Tamer: He keeps a "de-beaked" headcrab as a pet. Her name is Lamarr.
Honorary Uncle: On a corkboard in his lab, there's an arts-and-crafts collage of him made by a younger Alyx with "Uncle Kleiner" written beneath.
Nice Job Breaking It, Hero: It really wouldn't be inaccurate to lay the entire mess and its expansion packs on him. It was Lamarr who disrupted the teleporter, causing Breen to become aware of Freeman's restoration, which resulted in the Transhuman Forces being rallied, which led to... well, all of the death and destruction. All because he had to keep a frigging untameable brain-sucking alien monster as a pet.
Noodle Incident: It has something to do with the cat and the teleporter in his lab. Barney mentions the cat twice.
Oh, Crap!: When Alyx and Gordon make contact with him and Eli at the start of Episode One, Kleiner tries to calm Eli down under the belief that she and Gordon are safely out of the doomed city. When Alyx states that they are actually standing right next to the about-to-explode Citadel, Kleiner immediately joins Eli in his panic.
Omnidisciplinary Scientist: His expertise seems to be physics, but he is apparently responsible for the creation of the Mark V HEV suit, suggesting knowledge of mechanics as well. Somewhat justified as he did have 20 years to get aquainted with the field.
Performance Anxiety: Downplayed, but present. he's put in charge of delivering evacuation broadcasts and valuable exposition on the state of the war the Resistance is in, and is obviously nervous through his tone and breathing when he begins. He gradually begins to hit his stride to the point of delivering an inspiring speech to give hope to the rebels.
Pet's Homage Name: His "de-beaked" headcrab is named after Hedy Lamarr. It's both a bad Stealth Punand a Shout-Out to a classic actress—one who helped pioneer early wi-fi and cordless technologies.
Refuge in Audacity: Setting up a resistance research lab in the Combine's capitol city certainly took some chutzpah. No less, a research lab located right down the block from a major train station crawling with metrocops.
Rousing Speech: Delivers one to the people of City 17. Kleiner urges the remaining citizens to hold on to hope and fight back against the Combine, even when the odds seem stacked against them. Dr. Kleiner: For what the Combine fear the most is not any tangible human weapon, but our will. Our intellect. Our ability to respond selectively and rationally to every terror they turn against us.
The Smart Guy: He creates a short-ranged teleportation system that allows for transportation on the same planet. Something that the Combine haven't figured out themselves yet.
Voice of the Resistance: Becomes one temporarily when the Resistance hijacks Breen's public broadcast system. It's mostly to give instructions on how to evacuate City 17, but he does take some time to give an inspirational speech about finally taking back the planet which is pretty impressive for someone who admits he's not very good at public speaking. He also notes that the suppression field is down and now would be a good time contribute to "the revival of the species".