It depends on the Arduino and the USB keyboard.
Many, but not all, USB keyboards have the ability to also work as a PS/2 keyboard. If your keyboard has this PS/2 capability, then you can connect it directly to any Arduino board and use one of the PS/2 Arduino libraries to read the keypresses (and, with some of the libraries, even control the lights on the keyboard). If the keyboard comes with a USB to PS/2 adapter, then it has this capability. Keyboards that don't come with the adapter may also work, or not. I tested a high end mechanical keyboard, a high end mechanical numeric keypad, a cheapo HP keyboard, and a cheapo off-brand keyboard and all 4 worked, but my super cheap numeric keypad did not.
You can find more information about connecting PS/2 keyboards to an Arduino board here:
You don't need a PS/2 adapter for the USB keyboard. You can just cut the USB cable and connect the wires directly to your Arduino. The connections:
Red (Vcc) - 5V
White (Data-) - Data
Green (Data+) - Clock/IRQ
Black (Ground) - GND
Some of the more advanced Arduino boards have USB host capability, and thus are able to directly communicate with USB devices.