Authors defines the endgame differently. But by any definition, when each side has at most one piece besides their king, you're in an endgame. That is precisely how Dvoretsky and Flear define the final phase of the game. Others say it starts even sooner.
When does the endgame start?

I don't think there's any one pure endgame definition, but you know you are in an endgame if:
-- you want to activate your king.
-- you no longer automatically want the initiative but must calculate whether you want to lose a move or not.
Generally, if the Queens are off the board, I'm thinking endgame.

Does the endgame start after all the pieces are off the board?
Well, I couldn't imagine a game of chess continuing with no pieces on the board! JK
Some players might respond with "when the Queens come off" but this seems to be an overly-simplified definition. There are Queen endgames and the Queens can come off in the early middlegame. A definition that I read somewhere that I really like went something like this:
"The endgame ensues when the safety of the King stops being a central concern and the participation of the King as an active piece becomes an integral part of the game."
For some reason, I generally feel the endgame has started when each side has three or less pieces (not counting Kings and Pawns). I don't know why, I just feel that way.

In other words, when the kings can come out to play ^^
That's true, the second part of my quote is almost identical.
I really like the first half because I think it offers a great guide as to when you should bring your King out. Most beginners know that they should centralize their King in the endgame, but many bring it out too early and get into dangerous situations, or are overly cautious and lose valuable ground to the opponent's King. I struggled with this for quite awhile. It still takes experience to know when the right moment has come, but it is important to know what to look for. "When King safety stops being a central concern" hit home for me.

Ive heard the description that when both sides (or just one, I guess!) have 13 points or less remaining on the board, the endgame has begun. However, I prefer to use the King's role in play as my endgame guideline.

"The endgame ensues when the safety of the King stops being a central concern and the participation of the King as an active piece becomes an integral part of the game."
That is as concise a definition as there is. So BorgQueen got it right as well. Thanks for all the comments
Does the endgame start after all the pieces are off the board?