Sin is the breaking of the Law.
1 John 3:4 (KJV)
[SUP]4 [/SUP] Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.
We have all sinned at some point.
Romans 3:23 (KJV)
[SUP]23 [/SUP] For all have sinned, and come short of the glory of God;
Our righteousness however is not always about Law but about our covenant we are subject to. So whether a Jew is righteous can depend on whether he has observed the Mosaic Law to a standard that he will be deemed righteous by God. The more important part here is that even when one deemed righteous by a covenant, he still has sinned.
We all know that lust can be a sin, however it says no where in Mosaic Law that lust is a sin. So even when a Jew observes the Law to be righteous, he's still a sinner in front of the set of Law used in the final judgment.
We have to sin in terms of God's Law used for the final judgment, however we can be righteous when measured by a covenant we subject to. It is because a covenant contains God's grace. Christians are those who are subject to the New Covenant. We are sinners in front of God's Law, however we can be the righteous when measured by the New Covenant. In this New Covenant we are measured by faith and faith only, as the Covenant itself is free of a set of Law equivalent to the Mosaic Law given to the Jews.
That being said, we shouldn't continue to sin or else we may not be the righteous even when measured by our Covenant, as faith without works is dead. Our works are not for our salvation but a reflection of where our faith is. Without good works, it means that our faith is not the faith God would like us to have to make us righteous.