Oswald Acted Alone

As a history nerd and hater of conspiracy theories, here is the first of five reasons Lee Harvey Oswald and Oswald alone killed JFK.

Oswald Acted Guilty

Oswald displayed clear consciousness of guilt. Of the many employees at the Texas School Book Depository, only Oswald failed to show up at the roll call after the murder. Of the hundreds of thousands of people in DFW, Oswald is the only person to shoot and kill a policeman moments after the murder. These are the clear actions of a guilty person. 

The Only People Who Have a "Magic Bullet" Are the Conspiracy People
Conspiracy theorists have argued that there must have been more than one gunman because it is impossible that the bullet that went through President Kennedy's throat could have also wounded Governor Connally. As Oliver Stone featured in his movie, this would have required a "magic bullet" to pass through Kennedy, change direction in midair, then hit the governor. But all these conjectures assume that Connally was sitting directly in front of JFK, as in the first diagram. However, Connally was sitting in a seat in the limo that was actually slightly more inside the car, which means that he was not directly in front of JFK, but offset to the left, as the photo taken from behind clearly shows. Consequently, the bullet that passed through JFK did indeed hit Connally exactly as the third diagram shows. A final point about the "magic bullet." If the bullet that exited JFK's throat was not the bullet that hit Connally, then that bullet should have made a mark somewhere in the limo. There is no evidence of such a mark. Consequently, it is actually the conspiracy theorists who have a "magic bullet" - it magically disappeared without damaging the driver or the limo. 

Kennedy's Reaction is Consistent with Shots from the Rear
Conspiracy theorists believe that the reaction of the president to the fatal head shot, back and to the left, shows that he must have been shot by someone in front of him (aka in the grassy knoll). This belief is faulty for two reasons:
1) While it is impossible to see this on the Zapruder film in normal speed, the fact is that JFK did move forward when shot in the head. This can only be seen by watching the film frame by frame. But from frames 312 to 313 you can clearly see the head of the president move forward. You can watch this here: http://www.jfk-online.com/jfk100shot5.html
(warning - graphic footage)

2) The resultant sharp movement backward movement was caused by two factors: the "jet" effect after the impact, and the sudden nerve reaction caused by the massive brain trauma of the shot.

Oswald Was Capable of the Three Shots
It is very common for conspiracy theorists to argue that Oswald did not possess the skills to shoot the president with such accuracy. This is simply false, for several reasons:
1. The total time for all three shots is 8.4 seconds from the first to last shot, which means there was plenty of time to get off the three shots. 
2. Oswald was trained in weaponry in the Marines. HIs scores dropped from 212 (sharpshooter) to 191 (marksman) during his time in service, but he clearly possessed the proficiency to shoot the president.
3. Oswald missed with his first shot (frame 160 of the Zapruder film) completely, and was off target on his second shot (presumably he was aiming for the head rather than the president's back). His third shot was on target. For the last two shots, his target was relatively close: 59 yards and 88 yards, and in a clear line of sight.
4. And of course, the bullets that wounded the president were confirmed to come from Oswald's rifle, to the exclusion of all other rifles.

There Is No Evidence of A Shooter at the Grassy Knoll or Other Conspiracies
But of course there are conspiracy theories, and it would be impossible to disprove all of them. All anyone can do is point out the obvious nature of LHOs guilt, and the lack of evidence (not speculation) for the involvement of anyone else.

For example, many people have suggested there was a second shooter (making this a conspiracy by definition) in the grassy knoll on the other end of Elm Street. If there was one there, all we can say is, he completely missed! There were no entrance wounds to the front of the president, and no exit wounds to his back. And no marks of any other bullet anywhere. Further, there were no bullet casings found in the grassy knoll, and no hard evidence of any kind that a shooter was there. It is pure speculation.

Conspiracy theorists do not need evidence. All they need is two things: speculation about the motives others may have had to kill JFK, and questions about mysterious or unusual things that happened in connection with JFK's murder. Unlike TV crime shows, real life of much more messy, and there are always going to be unusual things that happen in an investigation. Many of these things are due to incompetence, and many are due to mere chance. But no amount of speculation, and no amount of anomalies, change change the hard evidence that clearly points to Oswald's guilt, not just beyond reasonable doubt, but beyond all doubt.

Conclusion
Yet most Americans believe there was some kind of conspiracy, some sort of coverup. In part this is due to the inherent distrust of government that is the birthright of all Americans. I don't trust the government, either! And part of this is due to the unwillingness to acknowledge that a single crazy person like Oswald could kill a beloved figure like President Kennedy. But the reality is that one lone nut can cause unimaginable harm, and that is exactly what Oswald did. Sadly, by propagating bizarre theories about JFK's assassination, conspiracy people have given Oswald a prestige such a wretched criminal never deserved. 

If you would like to get the definitive treatment of the murder of JFK, you have to get Vincent Bugliosi's Reclaiming History. Also, several years ago, a company produced an actual mock trial of Oswald, with Bugliosi as prosecutor and Gerry Spence as defense counsel. You can watch the entire thing online here.