Bearing in mind Mr Simpson was acquitted in his criminal trial of the murder of Nicole Brown Simpson and Ron Goldman (although he was found liable for wrongful death in the subsequent civil trial), any answer is of course conjecture and likely prone to bias on either side of the fence. That disclaimer aside, there is very compelling evidence to suggest that Simpson was in fact guilty of both murders. The following is a brief account of the main evidence against Simpson, and for the sake of brevity assumes that you are already familiar with the general background of the case and the main actors.

Key: Simpson = OJ Simpson; NBS = Nicole Brown Simpson; RG = Ronald Goldman

Blood and hair evidence

• Simpson's blood was found at the Bundy crime scene, in his Ford Bronco and at his home
• Simpson's bloody shoe prints were found at the crime scene
• Hairs found in a woollen cap at the crime scene were a forensic match for Simpson
• A bloody glove was found on a footpath at the rear of Simpson's home. The blood was a DNA match for Simpson and that of both victims. Hairs of both victims were also found on the glove, and microscopic fibres matched the carpet of Simpson's Bronco. The glove was a match for the other one found at the Bundy crime scene
• A pair of blood-spattered socks were found on Simpson's bedroom floor. The blood was a match for Simpson and NBS. This evidence proved to be controversial, as traces of EDTA (a blood preservative used when collecting samples) was detected in the blood, indicating possible contamination
• Blood of both victims was found in the Bronco

Circumstantial evidence

• On the night of the murders, Simpson sustained a very deep wound to a finger on his left hand. In fact not only the same night, but the precise hour that the crimes were committed. In his first police interview the day after, Simpson said that he could not recall how he had been cut. However, in subsequent testimony he claimed that he cut it while retrieving his cell phone from his car while rushing to catch his flight to Chicago
• Two independent witnesses swore that they saw Simpson's white Bronco, or a vehicle very similar to it, speed away from Nicole's street at the precise time that the murders are believed to have occurred
• The bloody footprints found at the crime scene were matched to a size 12 Bruno Magli shoe. These Italian designer shoes were so rare that only 299 pairs were sold in the USA up to that point. Photographic evidence of Simpson wearing these exact shoes were shown in the civil trial, despite Simpson previously denying that he ever owned them
• The bloody gloves were identical to a pair that NBS bought for her husband in 1990. Like the shoes these were very rare models, with only 200 pairs sold in that year
• Simpson had a long history of spousal abuse against his ex-wife. In their 17 year relationship, NBS had called the police 9 times to complain of domestic violence. Simpson was convicted in 1989 of spousal abuse and received community service
• NBS had confided in friends shortly before her murder that she feared Simpson would kill her one day. She also suspected that he was stalking her
• Two days after the murders, Simpson's defence team had him undergo a polygraph test. Knowing that whatever the outcome the test would be inadmissible as evidence, they hoped for a positive result that might be used to sway public opinion in favour of Simpson. In the polygraph, a score of -6 or less indicates deception while +6 indicates that the subject is telling the truth. Simpson failed the test miserably, scoring -24. In a report submitted to defence attorney Robert Shapiro, the test administrator Dennis Nellany interpreted the polygraph as an indication of Simpson's guilt in the murders. Unsurprisingly, the defence chose not to publish the results. The test eventually came to light during the 1996 civil trial
• When Simpson was notified via his lawyers that he was to be charged with the murders and to surrender at the police station, he instead absconded with his friend AC Cowlings, leaving what seemed to be a suicide note. When he was finally apprehended after the notorious Bronco chase, he was found with his passport, a gun, a fake beard, clean underwear and $8750 cash, which Cowlings said OJ had asked him to hold. A receipt found with the beard showed that it had been purchased two weeks prior to the murders
• A guard at the jail where Simpson was being held on remand, and in the room when Simpson talked to minister Rosey Grier, swore that he overheard Simpson shout "I didn't mean to do it. I'm sorry."
• Simpson had no alibi for the time of the murders. In varying accounts he claimed to either be asleep or chipping golf balls on his lawn alone in the dark

As far as motive is concerned, one can only speculate. The murders happened two years after a bitter and costly divorce. Simpson had tried to reconcile with his ex-wife numerous times after the separation, and although they did reunite once or twice, the relationship increasingly became more strained.

Simpson was known to be jealous and possessive of Nicole, and once spied on his ex-wife through her living room window while she made love to another man, afterwards confronting them. Five weeks prior to her death, NBS had told Simpson that she no longer desired to reconcile their marriage and that their estrangement was final.

On the day of the murders, Simpson attended his young daughter's school dance recital and had expected to join the Brown family for a meal at a local restaurant planned for that evening. However, after they had argued during a telephone call earlier that afternoon, NBS told Simpson that he was not welcome anymore to join them for dinner that night. Simpson was seen at the recital scowling, and according to the sister of NBS who was present, staring intently at Nicole from behind and generally acting unusually.

Sources:

Bugliosi, Vincent - Outrage: The Five Reasons Why O. J. Simpson Got Away with Murder

Toobin, Jeffrey - The Run of His Life: The People v. O. J. Simpson