This a question that I frequently hear, especially from folks at my Church. In short, the general answer is "Yes, you can sue in most cases."

The Bible does, however, forbid certain lawsuits, between believers in Jesus Christ. In the text of 1 Corinthians 6, we have a reference to lawsuits about grievances against "brothers" in the church. In context, here is the text:

¹ When one of you has a grievance against a brother, does he dare go to law before the unrighteous instead of the saints? ² Do you not know that the saints will judge the world? And if the world is to be judged by you, are you incompetent to try trivial cases? ³ Do you not know that we are to judge angels? How much more, matters pertaining to this life! ⁴ If then you have such cases, why do you lay them before those who are least esteemed by the church? ⁵ I say this to your shame. Can it be that there is no man among you wise enough to decide between members of the brotherhood, ⁶ but brother goes to law against brother, and that before unbelievers? ⁷ To have lawsuits at all with one another is defeat for you. Why not rather suffer wrong? Why not rather be defrauded? ⁸ But you yourselves wrong and defraud, and that even your own brethren. ⁹ Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived; neither the immoral, nor idolaters, nor adulterers, nor sexual perverts, ¹⁰ nor thieves, nor the greedy, nor drunkards, nor revilers, nor robbers will inherit the kingdom of God. ¹¹ And such were some of you. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and in the Spirit of our God. ¹²

As you can read the disputes that were addressed were believers who felt defrauded or wronged by others in that church at Corinth. Historians tell us that these disputes were about who would be overseers, and doctrinal issues among others. One can see why the Lord would be displeased with the example it would set if a church went to a regular court to settle a dispute over who would be a deacon, etc.

What about Lawsuits about Personal Injury, though?

The basis of our "Compensation for injury" theory of law has ancient roots. Indeed, read the text that follows from the Old Testament, Exodus 21:

When men strive together, and hurt a woman with child, so that there is a miscarriage, and yet no harm follows [to the mother], the one who hurt her shall be fined, according as the woman's husband shall lay upon him; and he shall pay as the judges determine.

Criminal penalties, such as the death penalty, are forbidden for accidents, and thus only civil actions remain, such as compensation. Read the following dealing with the ancient equivalent of accidentally running a red light and hurting someone: The axe head flying form the handle and striking your neighbor in Deuteronomy 19:

⁴ "This is the provision for the manslayer, who by fleeing there may save his life. If any one kills his neighbor unintentionally without having been at enmity with him in time past-- ⁵ as when a man goes into the forest with his neighbor to cut wood, and his hand swings the axe to cut down a tree, and the head slips from the handle and strikes his neighbor so that he dies--he may flee to one of these cities and save his life; ⁶ lest the avenger of blood in hot anger pursue the manslayer and overtake him, because the way is long, and wound him mortally, though the man did not deserve to die, since he was not at enmity with his neighbor in time past. ⁷

Finally, however, the Bible in Proverbs 25:8, encourages us to try and make out of court settlements, a practice I follow:

What your eyes have seen ⁸ do not hastily bring into court; for what will you do in the end, when your neighbor puts you to shame? ⁹ Argue your case with your neighbor himself, and do not disclose another's secret; ¹⁰ lest he who hears you bring shame upon you, and your ill repute have no end. ¹¹