My neighbor kissed my wife. I was pissed and wanted to punch him in his face. But I was able to suppress my anger.
If I did punch him, would that be okay? I saw people punch one another over this in movies. Kissing my wife is adultery right?
If I did punch him , would that be okay?
No, that would be Assault and Battery. If you did him serious injury you could face a charge of Grievous Bodily Harm. If you killed him, that would be murder.
If you are in the UK, Canada or Australia and you were charged with murder you could claim provocation in an attempt to have the charge reduced to Voluntary Manslaughter. If you were in the US you could attempt to argue "extreme emotional or mental distress" if you are in a state that has adopted the Model Penal Code for any of the charges; if successful your sentence would be reduced.
I saw people punch one another over this in movies.
And I saw aliens invading the Earth in the movies - what happens in the movies if not necessarily true.
Kissing my wife is adultery right?
No, extramarital sex is adultery. Notwithstanding, adultery is not illegal in common-law countries.
I'm pissed and don't know what to do?
I sympathise with you but this is not a legal question. Whatever is going on between you, your wife and your neighbour is a social situation; not a legal one.
The answer to your question depends:
In most jurisdictions you could use force to prevent a battery upon your wife (i.e., kissing). No jurisdiction I aware of allows you put take retribution by punching afterwards.