What kind of connotation does the expression "conspiracy theory" give you?

If a you get a negative connotation, you should know that according to the dictionary, a "conspiracy" is "an agreement to perform together an illegal, wrongful, or subversive act". You should also know that the U.S. governments official explanation of 9/11 events involve a conspiracy theory. According to the Bush administration, a group of Muslims had conspired to bring about a large-scale tragedy against the American people.