If you are a foreigner being sponsored for a family, or if you are an employment-based green-card holder being in a category of the applicant that faces annual numerical limits on visas, you might face a long wait.
The Violence Against Women Act ("VAWA") created a VAWA Cancellation of Removal for battered immigrants. It protects those who have been abused by their U.S. sponsor. Note that not all battered immigrant spouses can apply for it, because first, the immigration authorities must charge you with an immigration violation. It is usually an unlawful presence in the U.S. or overstaying a visa. If this happens, the immigration authorities will order you to appear in front of a judge.
If your spouse was abusive to you, you could still apply for U.S. lawful permanent residence independently. LPR status may be granted even without the help of the abusive sponsor.