Websurfing this morning I came across this page on ancestorhunt.com, a genealogy site, listing county jail inmate locators on the web for all 50 states. (This is just for county jails; the Texas prison inmate locator, BTW, is permanently linked in Grits' sidebar.) Here are the ones they listed for Texas:
Texas County Jail Inmates and Arrest Logs
I can see arguments both ways for whether or not to put this information online. It's all public record, lots of different people have uses for the information, and newspapers report that stuff all the time. On the other hand, putting names of people online whose cases haven't been adjudicated seems potentially problematic. At the end of the day, though, if public records aren't available online it only leaves open the door for private businesses to provide that service for a fee - why make the public pay to access data they already paid to generate?
Texas Arrest Warrants
Just to try out the databases (and to check on the relatives), I ran the name Henson through several of them. It turns out I haven't been arrested, at least lately. But in Harris County two of the four names that came up in the inmate locator had no charges listed and had been shifted to the "inactive file." I'm not sure I see a reason for keeping their names in a public, online database.
UPDATE: See also Travis County's Jail Inmate Locator, Dallas' Current Inmate Listing, and the El Paso Sheriff's Inmate Log Search. Leave links to others in the comments if you know of them.