Yes, it's the current that kills (if enough of it passes through the right path), but the voltage creates that current:
I (current) = V (voltage) / R (resistance)
The lower your skin/body resistance (wet skin has much lower resistance than dry skin) or the higher the voltage, the higher the current.
Lower voltages often aren't as dangerous for 2 reasons:
1) Whatever your body's resistance, the current is lower 2) The low voltage is often supplied by batteries or transformers with lower current capacity (high internal resistance) -- if your body tries to sink a lot of current (low body resistance), the voltage drops significantly. On the other hand, a car battery can supply hundreds of amps at 12V, and you could easily electrocute yourself with one if your body resistance/path is right.Josh