This question has been debated in great length, but there is no clear answer. However, Chase has been quoted as saying everything we need to understand the ending is in the episode itself. He has stated that we are too spoon-fed as an audience, as in tell them what they're going to see, show it to them, then tell them what they've just seen. Chase felt upset that fans seemed to want a bloody death for Tony after cheering him on for 8 years.
There are several clues in The Sopranos: Made in America (#6.21) indicating that Tony Soprano was killed:
* The previous episode contains a flashback to a scene from The Sopranos: Soprano Home Movies (#6.13) in which Bobby 'Bacala' Baccalieri and Tony Soprano discuss what it's like being killed, saying "in our line of work, it's always out there. You probably don't even hear it when it happens". While the flashback may or may not be referring to this scene, the cut to black and complete silence would be exactly what Bobby described.
*Chase sets up a pattern of point of view shots where we see a shot of Tony, then his point of view of someone walking into the restaurant when the bell on the door rings, and then the reaction shot. Following this pattern, we hear the bell ring as Meadow opens the door, we get the shot of Tony, then right when we should see Meadow walking in from Tony's point of view, we get black nothingness.
* The screen abruptly cuts to black and all sound mutes as opposed to the fade in most other episodes that keeps the soundtrack running (which goes hand in hand with the above-mentioned discussion).
* The person staring at Tony Soprano and walking to the bathroom is significant enough to be credited, with a special mention to his "Member's Only" jacket. "Member's Only" is the episode in which Tony got shot, and is a reference to being in the mob, as well as to the character in "Member's Only" who kills himself when Tony won't let him move his family to Florida. The "Member's Only" man simply can be seen to represent everyone Tony has wronged throughout his life. He is also the only patron we see walking into the diner before we get Tony's point of view of him walking into the diner followed by AJ.
* A hitman walking into a bathroom to retrieve his weapon reminds of a famous scene from The Godfather.
* It's the only time in the series Tony is seen peeling an orange, an obvious reference to the Godfather movies where oranges are closely associated with an approaching death or being shot.
* The scene has been edited in a way that builds up tension, which naturally leads the audience on to believe something momentous is going to happen (which may or may not be the case).
* Many of the patrons in the diner represent an event from previous episodes that involved killing someone.
* Tony Soprano often spoke of in Soprano Home Movies, All Debts Public and Private, and The Happy Wanderer, that there are only two ways out for a boss. Dead or in Jail. We saw Johnny Sack, another boss, go the route going to jail. We also saw Little Carmine step away from the title of Boss to enjoy and live his life. So it would make sense that we see Tony take the other path, death.
However, there are also several things hinting that [spoiler]nothing happened to Tony Soprano:
* We never actually see anything happen other than suggestive editing - we don't even see a gun. Or to put it more simply, we do not see Tony Soprano die, therefore when the show ended, Tony Soprano was still alive.
* The lyrics of the infamous Journey song indicate that life goes on despite all the trouble.
* The jacket of the Member's Only guy doesn't have a logo on it. Maybe that means that he - like the jacket - is an imitation, not the real thing.
* There was no reason for to be killed - the hit on Phil had been sanctioned by the Lupertazzi Family. (even so this is discussable because there where many variables in the way the hit went down. Phil was killed in front of his family and other witnesses and his head got crushed by his own SUV. This method of killing may have angered the Lupertazzi Family prompting a possible violent retaliation.)
The general consensus that most people can agree with is that the last scene shows the audience how is feeling every day: In an everyday situation like eating dinner, everybody around him could be out to kill him. He is constantly living in paranoia and the fear that anybody who looks at him or brushes past him could be a killer. Whenever anybody enters the diner, Tony Soprano looks up to glances up to see if that person is a threat. The last season has had an emphasis on the downside of the mob life - Johnny Sack dying in prison with no money, leaving his widow penniless, people even in high ranks getting killed, Tony Soprano killing his own nephew in a despicable way. The final scene shows the sad life of those who survive - living in constant fear, facing death or prison. However, this does not hold up well under scrutiny because when looking at the final scene we only see shots of most of the patrons in the diner from a third person perspective. It is only when the bell rings on the door that we get Tony's point of view of someone entering the diner. When we see the other patrons in the diner, it is only through third person and Tony is actually looking down at his menu for most of these shots. This explains the ending in that right when we should get Tony's point of view of Meadow walking into the diner we see black nothingness and the music cuts out. Apparently Chase actually wanted the black nothingness to be it and not even have credits, but HBO forced him to include credits.