Answer:
Every US State has its own State Supreme Court (except Texas, which has two) and the US has one Federal level Supreme Court. Total: 52.
EDIT:
It depends on what you mean by "Supreme Court." It's true that each state has a high court, although some states don't call their highest court the "Supreme Court." New York, for example, calls its highest court the "New York Court of Appeals" (the "Supreme Court" usually refers to trial level courts in New York). As the original poster noted, Texas has two, co-equal highest courts: The Supreme Court of Texas handles appeals in civil, juvenile, and family matters, and the Court of Criminal Appeals is the court of last resort for criminal matters. The Texas Supreme Court, though, manages and oversees the promulgation of most of the states' legal rules and oversees the bar.
There's a similar relationship with two high courts in Oklahoma.
So, in one way, the answer could be: 51 -- 50 "highest" state courts plus the United States Supreme Court.
Or the answer could be: 53 (with two co-equal highest courts in Texas and Oklahoma (that's 4), plus 48 other highest state courts, plus the U.S. Supreme Court).
And if you wanted states that called their highest courts "supreme courts," that would take a bit longer to find out.
For more information, see Related Links, below.