JFK's assassination is far too fishy for me to accept the official explanation, so while it's not enough to say there was some big conspiracy I don't think things went down as exactly as they said for whatever reason.
The conspiracy around the Titanic doesn't seem that far fetched, not that they deliberately sunk it but I can believe they used another similar looking ship if the Titanic wasn't ready for use, especially if there was a lot of money riding on it.
Don't believe the moon landing was faked for one moment since the theories either require too many people to know, or that they're so elaborate that it would have been easier for NASA to just go to the moon anyway, without of course forgetting that not a single person has come forward as a whistle blowing since and well dead people don't have much to fear...
Most recent of course is 9/11, I used to assign some credibility to the theories thanks to Loose Change, but then changed my mind when they were thoroughly destroyed and debunked, that doesn't necessarily mean the conspiracy theorists are wrong just that they don't have any current evidence to suggest they're right, and there is how the towers fell - that is fishy.