Nazi Hunter

Kaplan: I lost my first wife, my first family. Two beautiful little girls. In the war, in the camps. I thought for a long time the loss would kill me but, I survived.
Heller: How?
Kaplan: By creating a ritual to keep me alive. To survive the death of people close to you, you need a ritual. A ritual for revenge is what I made. I thought about it and planned it every waking moment. When I got out I spent three years tracking down the doctor who sent them to the camps.
Heller: Did you find him?
Kaplan: I found him, yes.
Heller: What did... what did you do?
Kaplan: I created one last ritual. With these hands I strangled him.
Heller: It didn't bring them back from the dead.
Kaplan: No, it brought me back from the dead!

—The Amateur (1981)

We will be doing one thing and one thing only...killin' Nazis!

—Lt. Aldo Raine, Inglorious Basterds

Someone who dedicates their life to hunting down ex-Nazis, or is dedicated to hunting down one particular Nazi because of what they did in World War Two (Note: this trope doesn't apply just because the antagonist happens to be an ex-Nazi). Often a Badass Israeli who might be working for Mossad, a result of the high-profile kidnapping of Adolf Eichmann from Argentinia in 1960. In reality Mossad stopped chasing war criminals not long after this event, as more urgent threats to Israel took priority.

Expect the former Nazi to be living in a Banana Republic in his well-guarded mansion financed by Nazi Gold, from which he plots the return of the Third Reich. Hardly Truth in Television, as genuine war criminals go to some trouble to avoid drawing attention to themselves.

Something of a Dead Horse Trope these days, as anyone who served in World War Two gets too long in the tooth to be anything other than a Nazi Grandpa, and the end of the Cold War dramatically expanded the choice of stock villains.

Very common in Nazisploitation films.

Examples of Nazi Hunter include:

Comic Books

In the Marvel Universe, Silver Sable's father did this, with the Wild Pack originally being established as a Nazi hunting group. In the modern era, Silver and the Pack have become little more than mercenaries as there are much fewer surviving Nazis, but when they do show up, they still hunt them down.
There was an extended comic story in National Lampoon magazine about "Gunnar Von Weissen," an ex-Nazi who hunted former concentration camp prisoners, a la Wiesenthal.
There was an indie comic called Manimal (no, not that one) about a Superhero who tracks down and slays the Nazis responsible for turning him into a freak. This comic was reviewed by The Cinema Snob and Linkara.
Hellboy tracked down Nazis after the war and even killed Adolf Hitler himself. Some of these Nazis are still around and he expresses his digust of Nazis everytime he sees them.
Captain America (comics) himself continues to do this to this day, thanks to the Red Skull being very hard to kill.
Rebeccah's sister in Requiem Chevalier Vampire. She kills Otto (an old Nazi hiding in Argentina at that point), sending him to Resurection.
In the 80's, Magneto joined the ranks of several Marvel villains in the Acts of Vengeance Crossover simply so that he could get close to the Red Skull and bury him alive. Magneto was a Holocaust survivor so there was no love lost between him and the Skull.
The Sin City short story Rats features an elderly Nazi war criminal, apparently living in secret in America. A mysterious Nazi Hunter soon kicks in the door and kills him by shoving him in the oven. It is speculated that the Nazi Hunter in this story is a young Mob Boss Wallenquist, a German mafia leader.
A back-up story in an issue of Savage Dragon involved the Super Patriot tracking down a cult of ninja cyborg Nazis. Since he was a WWII vet, he took great pleasure in blowing them apart.

Film

Erik Lensherr (AKA Magneto) is this in the beginning of X-Men: First Class. Based on his backstory from the comics (but not the movies), Badass Israeli is plausible.
Night Gallery pilot film, episode "Escape Route". A Nazi war criminal living in South America is pursued by Israeli agents, including a man he tortured at Auschwitz.
Inglorious Basterds features a squad of JEWISH-AMERICAN-SOLDIERS! killin' Nazi officials and soldiers during WW 2 as opposed to after it. One of their member also happens to be a Hunter of His Own Kind, a former German soldier that developed a taste for killing Nazis himself.
SLC Punk! has a modern take on this; the main characters find Neo-Nazi punks and beat them up. This is mostly due to the Neo-Nazis calling themselves punks rather than any moral reasons.
The Debt follows three young Mossad agents attempting to kidnap a Captain Ersatz version of Dr. Mengele from East Berlin in the 60's.
In the French movie (and remake) Marie-Octobre, the target is not the former Nazi himself, who was simply an enemy soldier: the problem is that said German revealed the presence of a traitor in the former resistance movement.
Walk on Water

Literature

The Odessa File by Frederick Forsyth. Has Simon Wiesenthal as a cameo character.
The Boys from Brazil by Ira Levin. The protagonist is an obvious Wiesenthal Expy.
Subverted in "Cobra" by Andrew Vachss. Burke motivates The Mole (who's Jewish) by saying the people he's chasing are Nazis, when the only Nazis he knows are pathetic wannabies to whom he sells copies of Hitler's final speech (actually Simon Wiesenthal addressing a crowd of Holocaust victims).
Subverted in "The Statement" by Brian Moore. The Villain Protagonist (a former member of the Vichy police) is not being hunted down by Jewish assassins as he thinks, but his own colleagues (now high-ranking police officers) who have hired the men (common criminals with Jewish backgrounds) so he won't be arrested and testify against them.

Live-Action TV

Kessler, the sequel to Secret Army, in which the title character is pursued by a German police officer, and a young Israeli woman seeking revenge for her roommate being killed by neo-Nazi thugs.
Airwolf ("Fight Like a Dove"). The daughter of a Nazi hunter murdered by an ex-Nazi Arms Dealer gets their help to attack the Big Bad in his fortress in Paraguay.
Heartbeat ("Going Home"). A German-American called Victor Kellerman tries to kill a local resident, after spending years trying to track down this 'friend' who confiscated his wealth and sent him to a concentration camp. He's finally able to track him down when the man's son sells a valuable stamp which used to belong to Kellerman.
The 2007 TV adaptation of the Miss Marple story At Bertram's Hotel turns Malinowski (a racecar driver in the novel!) into a Nazi hunter.
Sue Sylvester's mother Doris on Glee.

Real Life

Simon Wiesenthal
- The Simon Wiesenthal Center has recently started to realize that Nazi war criminals are soon going to be all dead, so they've redirected toward hate groups, and toward anybody accused of antisemitism, except, oddly, Argentine dictators who openly praise Adolf Hitler.
The Avengers. No, not these ones.
Efraim Zuroff
Serge and Beate Klarsfeld
In 1990 a 66-year old Italian immigrant called Giuseppe Bonfanti (who had been living in Brazil since World War II) returned to his hometown and used a pickaxe to kill Giuseppe Oppici, a 68-year old former fascist who during the war had helped burn down Bonfanti's farm and slaughter his livestock, in retaliation for his partisan activites.
Hunting Nazis was one of the first tasks carried out by the Mossad.