I had that problem some time ago with 30000+ gallons water usage.
I also saw no signs of obvious leakage- no excessively green or fast growing lawn areas. No standing water anywhere.
I complained and they came out to check the meter (which unfortunately don't fail very often). What really is a bad deal is anything after the meter (on the house side) is considered your problem.
I finally had to call somebody out and it turns out that I was losing about .5 gallon per minute! Still, I saw no obvious signs of a problem other than a huge water bill.
As it turns out, I had a crack in a line under the driveway and the water was escaping into the water table and never making it to the surface. Most of the time, water lines are usually buried about 18-24" deep but in my case, where the break was, was 6 ft. under the surface.
They had to tear up my driveway and replace the line from the meter to the house. $1300 later, and a dead yard because I couldn't afford to water it, my bill is again around $40. (The grass has recovered nicely)

If there was any good news that occured during this problem, it was the fact that once I fixed the leak, thereby proving the water didn't go through the sewer (which was almost more than the water cost itself), the Municipal Utilities District gave me a credit which paid my bill for over 5 months.

Best of luck with this problem and hopefully they misread your meter or it is failing. Somebody on this thread mentioned shutting the water off and checking the meter- I suggest that you do this also and if it is still spinning, you definitely have a leak.