The main conspiracy points of this incident are outlined below. (They are in no particular order).

Conspiracy	Notes
1) She committed suicide.	This is the official cause of death ('probable suicide'). However conspiracy lovers say that it is not consistent with forensic facts. She died, apparently, of a rectally administered barbiturate enema (source crimelibrary.com) which, if true, could not have been administered by herself. Recently published transcripts from conversations with her psychiatrist, John Miner, indicate that Monroe was not suicidal, and was making plans for her future, including a remarriage to Joe DiMaggio. "I feel certain I'll win an Oscar for one or more of my Shakespeare women," Monroe says according to the transcript.
2) She died as a result of a simple accident.	Conspiracy lovers have a field day on this theory. This is why: Marilyn had two physicians (Dr. Ralph Greenson and Dr. Hyman Engelberg) both were attempting to get her off Nembutal, substituting chloral hydrate to help her sleep. It is possible, the story goes, that the fatal enema was given to Marilyn by mistake as Dr Greenson (now dead himself, so cant respond) was not aware that Monroe had been taking Nembutal capsules during the day. Dr. Engelberg was apparently having marital problems at the time which might explain why he didn't communicate his prescription details. Monroe, too, may not have realized that Nembutal would have a reaction against the chloral hydrate. So, who administered the enema? crimelibrary.com: "...it had to be Eunice Murray, who, like Greenson, had no inkling that the sedative enema would be fatal. Any doctor might be loath to admit to himself or others that he had made such a significant mistake in such a high-profile patient, especially since Marilyn appeared drugged during the afternoon. Also, if Eunice was the person who administered the enema, it would be natural for her to try to protect herself and Dr. Greenson by pretending that no such procedure was given to Marilyn."
3) Marilyn Monroe was having an affair with John F Kennedy (and possibly Robert) and she was about to go public with what she knew. She was killed by 'government agents' to protect the president.	Marilyn knew a lot about JFK: his marital infidelities (at the time hushed up) and other private matters. She had his notes and letters and was privy to Kennedy's involvement with Sam Giancana, the mob leader. The Kennedy brothers had discussed national security matters with Monroe. It is reasonable for the Kennedy administration to want to at least try to cover up the liason with Monroe, but did they?
4) Following on from 3) Robert Kennedy, the president's brother, went to see Monroe the night she died to tell her that President Kennedy did not want to see her anymore.	There are witnesses, including a policeman, who places Robert Kennedy in the area at the time of her death. It is possible after this rejection her good mood, seen earlier in the day, changed and she killed herself. It is also alleged that someobody removed a diary and an incriminating note from Monroe's home at 12305 Fifth Helena Drive, Brentwood.
5) Peter Lawford (Bobby Kennedy's brother in law) and Pat Newcomb went to Marilyn Monroe's house on the night she died.	This is seen as further evidence of a Kennedy connection.
6) Bobby Kennedy himself murdered Marilyn Monroe.	No, not likely at all. Robert Kennedy was a highly respected Attorney General with an unimpeachable integrity with little mystery surrounding him, as opposed to Monroe who had many secrets.
7) Marilyn was killed by the mafia as punishment to the Kennedy's for their attacks on them, and to expose Kennedy's philandering.	Definite motive, but probably difficult to accomplish that night in view of the number of people about.

Postscript: Monroe was finally laid to rest on August 8, 1962, in Los Angeles' Westwood Memorial Park in the Corridor of Memories.