United States' law does not establish any precedent in this area, so it is up to the individual states to set the legal environment. That said, as others have noted, this usually depends on the employer's policies and/or your employment agreement.
In my experience (25+ years in technical jobs), unused vacation time is usually paid out when you leave a job. However, as mhoran_psprep's answer indicates, many employers set some sort of maximum on the amount you can accumulate or how much you can carry from one calendar year to the next.
A quick web search turned up a write up summarizing California law for this issue. Generally, the law views vacation time as part of your wages, so you would be paid for it upon leaving. However, this can be modified by a collective bargaining agreement. Question 10 on that page specifically addresses this issue.