In the two examples you provide, the adverb "again" servers two different functions.
In "here we go again" it is modifying the verb "go". There should not be a comma between a verb and its adverb, regardless of whether it's at the end of the sentence or not. Here are some more examples:
Please come again.
I will do it again.
Trying again was not a good idea.
In "What is the definition of irony, again?", the word again is modifying the independent clause "what is the definition of irony". It is making a conceptual connection between this sentence and a previous one. It's not a separate clause, but a type of conjunction (a conjunctive adverb). It needs to be preceded or offset by commas, regardless of where it is in the sentence. Here are more examples:
Again, the definition of irony is [...].
Why is it, again, that you're looking up this word?