What happened to Ananias and Sapphira after death? Acts 5:1-11 (NIV)
  
  1Now a man named Ananias, together with his wife Sapphira, also sold a piece of property. 2With his wife’s full knowledge he kept back part of the money for himself, but brought the rest and put it at the apostles’ feet.  3Then Peter said, “Ananias, how is it that Satan has so filled your heart that you have lied to the Holy Spirit and have kept for yourself some of the money you received for the land? 4Didn't it belong to you before it was sold? And after it was sold, wasn’t the money at your disposal? What made you think of doing such a thing? You have not lied just to human beings but to God.”
  
  5When Ananias heard this, he fell down and died. And great fear seized all who heard what had happened. 6Then some young men came forward, wrapped up his body, and carried him out and buried him.
  
  7About three hours later his wife came in, not knowing what had happened. 8Peter asked her, “Tell me, is this the price you and Ananias got for the land?”
  
  “Yes,” she said, “that is the price.”
  
  9Peter said to her, “How could you conspire to test the Spirit of the Lord? Listen! The feet of the men who buried your husband are at the door, and they will carry you out also.”
  
  10At that moment she fell down at his feet and died. Then the young men came in and, finding her dead, carried her out and buried her beside her husband. 11Great fear seized the whole church and all who heard about these events.


This is the only passage that I know of in the New Testament that tells us of Christians being put to death. As far as I understand, it was God that put them to death for lying to the Holy Spirit.

My question is what might have happened to them after their sudden death. Did they go directly to hell, or did they go to heaven? Was their death a kind of instant judgement that sent them away from God and directly to hell?
We don't know
The Bible doesn't tell us.  The only answer I can give is a tautology - if they were saved, then they went to heaven.  But the Bible doesn't tell us whether they were saved.
However, it should be noted that the nature of their punishment does not rule out the possibility of their salvation.  Consider 1 Corinthians 5:1-5 (NASB):

It is actually reported that there is immorality among you, and immorality of such a kind as does not exist even among the Gentiles, that someone has his father’s wife. You have become arrogant and have not mourned instead, so that the one who had done this deed would be removed from your midst.
For I, on my part, though absent in body but present in spirit, have already judged him who has so committed this, as though I were present. In the name of our Lord Jesus, when you are assembled, and I with you in spirit, with the power of our Lord Jesus, I have decided to deliver such a one to Satan for the destruction of his flesh, so that his spirit may be saved in the day of the Lord Jesus.

Although the meaning of &quot;destruction of his flesh&quot; is debated, one possible interpretation is that this person was being sentenced to death.  Yet it is made clear that, despite the severity of the punishment, the man himself was saved.
But the question remains of whether Ananias and Sapphira were saved in the first place, as nothing in the text rules out their salvation, or indicates their possession of it.