Permanent residency (the "green card") allows you to live and work permanently in the US and is the step before citizenship. There are multiple categories for obtaining it, and many people who believe they have no options actually do.
Through a US Citizen or Resident Family Member
Family categories include: citizens petitioning for spouse, children, parents or siblings (the first three categories are immediate or high priority); and permanent residents who can petition for their spouse and unmarried children. "Preference" categories have waiting lists that can last years, for Mexican citizens, historical waits have been 10-20+ years for some categories.
Through Employment
If you have a willing employer to sponsor you or have extraordinary abilities in your field, you may qualify for an employment-based green card. The process generally requires labor certification (PERM) demonstrating no available American workers for the position.
Special Paths for the Hispanic Community
Important special categories include: VAWA, for domestic violence victims with an abusive US citizen or resident family member; U Visa, for crime victims who cooperated with authorities (leads to green card at 3 years); T Visa, for human trafficking victims; and NACARA, for certain Central American immigrants. An attorney can identify which category, if any, applies to your specific situation.