This is a question that comes up regularly with folks who come to visit me in my office. I generally point them to 1 John 3.9...
No one born of God makes a practice of sinning, for God's seed abides in him, and he cannot keep on sinning because he has been born of God.
Pretty simple, right? If you're born again, you don't sin.
The ESV, which is my translation of choice, does a good job of helping us understand what John is after there. He's obviously not talking about never sinning. Even John, the author, fell down before angels in worship in Revelation before being told to get up and to worship God (19.10).
What he is talking about is practicing sinning or continuing in sin. When the trajectory of my life is measured, do I point in the direction of holiness, righteousness, goodness, justice, and love? Am I experiencing the transformational power of the Spirit of God living within me and making me into a new person as I work out my salvation with fear and trembling (Phil. 2.12-13)? Is there a sense in which I love what God loves and don't love what He doesn't love? Has my allegiance turned toward Him, albeit imperfectly? Is the compass of my life generally pointed Godward?
In other words, do I look like I'm a part of His family?
After all, that's what being born again means. We're born into the family of God where He becomes our Father by adoption through Jesus Christ (Eph. 1.5). So if I'm part of His family, I'll start to look like Him (Eph. 5.1).
But that's just me thinking thoughts...