Why some verbs with no prep. take the dative (danken) and others the accusative (belügen)?
Some german verbs take the dative (ex. danken, vertrauen, verzeihen, gratulieren, raten, vergeben), as we note in the following setences:
Ich danke DIR. Ich vertraue DIR. Ich verzeihe DIR...

But some use the accusative (ex. belügen, beraten, verehren):
Ich belüge DICH. Ich berate DICH. Ich verehre DICH.

I was wondering if there is a rule to distinguish these two kinds of verbs that take only one complement (not like geben, for ex., that takes two complements) and have no preposition that determines the case (ex., für, gegen, aus, bei).

Please, please let there be a rule for this (:P) and, if not, let there be some nice table that summarizes this.

Question

Why some verbs with no prep. take the dative (danken) and others the accusative (belügen)?
Some german verbs take the dative (ex. danken, vertrauen, verzeihen, gratulieren, raten, vergeben), as we note in the following setences:
Ich danke DIR. Ich vertraue DIR. Ich verzeihe DIR...

But some use the accusative (ex. belügen, beraten, verehren):
Ich belüge DICH. Ich berate DICH. Ich verehre DICH.

I was wondering if there is a rule to distinguish these two kinds of verbs that take only one complement (not like geben, for ex., that takes two complements) and have no preposition that determines the case (ex., für, gegen, aus, bei).

Please, please let there be a rule for this (:P) and, if not, let there be some nice table that summarizes this.

Answer

There is something like a rule. When you can omit the object and the remaining sentence makes sense then you use dative for this object (intransitive verbs). You can't form the passive voice with this kind of sentences.

Verbs with accusative objects are called transitive Verbs. You can form passive voice.

Of course, there are some exceptions ;)

Answer

No, as far as I can tell, there's no rule; you just have to learn which verb requires which case. Searching for things like "Verb Dativ Akkusativ" leads you to plenty of lists.