Nominativ
The list of verbs, that need an object in nominative case is short. You can call this object a Nominativobjekt, but the more common term is Gleichsetzungsnominativ (nominative of equality).
- sein
Hans ist Lehrer.
Hans is teacher.
- werden
Jürgen wird Arzt.
Jürgen becomes a doctor.
- bleiben
Walter bleibt ein Dummkopf.
Walter stays a fool.
- heißen
Ich heiße Hubert.
My name is Hubert.
- (zu sein) scheinen
Lisa scheint die Anführerin zu sein.
Lisa seems to be the leader.
- gelten (als)
Helmut gilt als Draufgänger.
Helmut is considered to be a daredevil.
- (sich) fühlen (als)
Donald fühlt sich als der Herrscher der Welt.
Donald feels like the ruler of the world.
- (sich) erweisen (als)
Das erwies sich als Fehler.
That turned out to be a mistake.
- (sich) entpuppen (als)
Das Paket entpuppte sich als eine Bombe.
The package turned out to be a bomb.
- (sich) dünken (outdated)
Unser Chef dünkt sich etwas Besseres.
Our boss thinks to be something better.
Genitiv
Genitive case often appears inside a nominal group as a possessive attribute of another noun, but there are also lots of other attributive usages of genitive case inside of nominal phrases. But you asked for verbs that need genitive objects, and there are no verbs inside of nominal phrases, so in most cases when you see a noun or a phrase in genitive case, this case is not ruled by a verb.
But there are still some verbs, that need a genitive object, and those verbs are rare too. Note, that many of them also can take a prepositional object instead of a genitive object.
- bedürfen
Dieser Umstand bedarf einer Untersuchung.
This circumstance requires an investigation.
- entbehren
Diese Behauptung entbehrt jeder Grundlage.
This assertion lacks any basis.
- ermangeln
Seine Aussagen ermangeln eines Beweises.
His statements lack proof.
- gedenken
Wir gedenken der Toten.
We commemorate the dead.
- harren
Wir harren deiner.
We are waiting for you.
- spotten
Das spottet jeder Beschreibung.
It beggars belief.
- (sich) annehmen
Irene hat sich seiner Kinder angenommen.
Irene has taken care of his children.
- (sich) bedienen
Er bedient sich des Messers.
He uses the knife.
- (sich) besinnen
Der Priester besann sich seines Gelöbnisses.
The priest remembered his vow.
- (sich) erfreuen (veraltet auch: sich freuen)
Susanne erfreute sich des warmen Wetters.
Susanne enjoyed the warm weather.
- (sich) erinnern
Er erinnert sich deiner nicht mehr.
He does not remember you anymore.
- (sich) rühmen
Er rühmte sich auch noch der Tat.
He even boasted of the act.
- (sich) schämen
Schämst du dich meiner?
Are you ashamed of me?
- (jemanden) (einer Sache) berauben
Er hat mich meines Bargeldes beraubt.
He robbed my cash.
- (jemanden) (einer Position) entheben
Der Kanzler wurde seines Amtes enthoben.
The chancellor was dismissed from office.
- (jemanden) (eines Ortes) verweisen
Der Rüpel wurde des Lokals verwiesen.
The ruffian was expelled from the pub.
In the next examples you will find groups of words, that might look like nominal phrases at first glance (like der Vater des Kindes = the father of the child), but in fact are a accusative object followed by a genitive object. All this examples occur when talking about crimes, so this special kind of genitive case is called genitivus criminis (genitive of crime). But it is not an attribute of any noun, but really an object that is ruled by the verb.
- (jemanden) (einer Tat) verdächtigen
Der Ermittler verdächtigte den Tankwart des Mordes.
The investigator suspected the attendant of the murder.
The following verbs work exactly like verdächtigen:
- anklagen (to accuse)
- beschuldigen (to accuse)
- bezichtigen (to accuse)
- zeihen (outdated) (to accuse)
- überführen (to find guilty)
Dativ und Akkusativ
The rest of the more than 14,000 German verbs need either no object (altern, schlafen, wachsen, ...) or an object in dative (gehören, vertrauen, nützen, ...) or accusative case (haben, kaufen, fragen, ...) or even both (geben, schenken, wünschen, ...). There are also verbs that can take two accusative objects (lehren, nennen, kosten, ...). (Verbs that take a genitive and an accusative object are already listed above.)
Since this place here is not appropriate to list 14,000 verbs, i have to ask you to search for them in your own.
There are patterns that cover some verbs, but most verbs do fit in such patterns, so I think the best way is to do what all native speakers did: Learn for each verb which case it needs for its objects.
