Is Hamlet's father good or bad?
I like to read this play as being similar in its dynamics to the Greek story of Orestes and Antigone who kill their mother, Clytemnestra, and her lover to avenge their father's death (Agamemnon).
Hamlet's dilemma is very similar to that of Orestes and Antigone. Justice demands that vengeance be taken on the murderer, yet justice can only be served by committing the crime of matricide.
Seen in this light, Hamlet's father is merely a spokesperson for justice - an embodiment of the social demand that the crime of his murder be balanced or accounted for in some way. He is not good or bad, but represents an unthinking and uncompromising force.
It is due to this unthinking, uncompromising, absolute nature that Hamlet, like Orestes and Antigone, has not real way out of his problem. There is no way to ignore the "natural" demand for justice on behalf of the murdered. But there is no way to soften the fact that this justice will result in another great and nearly unthinkable crime.
The Ghost urges revenge on his killer, Claudius. This would seem honourable to an Elizabethan audience and to many in a modern audience too. The Ghost is not evil because he does not want revenge on Gertrude; indeed he wants Hamlet to help her, 'step between her and her fighting soul!'
Hamlet questions the nature of the Ghost and thinks it might be evil not because of what it's demanding; it's more to do with the fact that he questions everything, and as we all know thinks too much!
I think you could argue that Hamlet's father was wrong to ask his son to avenge his death. He put Hamlet in a difficult position, and one that Hamlet might have been too young or fragile to easily cope with.
Because good and bad are relative terms, they are not the best way to describe the ghost; the ghost of Hamlet's father appears to him to tell him how he really died. He then proceeds to get Hamlet to avenge his father. Because this advocates the murder of the assassin/usurper, we might think him to be bad, but he is only promoting justice - which would make him good. In the end, it is up to the individual to decide whether they see him as good or bad.
Hamlet's father's gost comes that is the bad omen.It is the source that increased doubt between mother and son.Besides,it made the Hamlet mad and atlast snatched the life,beloved etc. So,his father is bad.