HI I'VE BOUT A NEW LAPTOP AND PLUGGED IN MY mAXTOR one touch 4 and the laptop is not recognising it. Is it because my pc was xp and this laptop is vista? Help please

One or more of the hints below will probably sort out most USB problems with most USB portable / external hard drives and OTHER devices (though not always)

A few things to check but assumes USB and Windows for other interfaces / operating systems (mac/ Linux) similar steps may be adapted to suit.

1. Ensure it is connected directly to the computer to a USB 2.0 port not a USB 1.0 port as this can have effects on performance and reliability

2. Use only the cables that came with it NOT one that fits that may have been lying around or is longer. Not all USB cables are equal even though they should be)

3. Do not connect through an external USB HUB unless that hub is USB 2.0 AND has its own power supply.

4. Use ONLY the power supply that came with it if it has an external power supply Don’t use any other unless you know it has both the same voltage and current rating e.g. 12V 500mA anything rated below that would not work properly.

5. Always use the same port for connecting your devices. Some devices do not like being switched about. If switched they may want to install software / drivers again. This can be especially true if you move a HUB to another port
6. For FLASH DRIVES you should ensure that the device is set for "quick removal" using the drive control panel properties or use the USB "Safely Remove Hardware" option. If you dont do this there is a very strong chance that any files you transfer may not be there when you plug into another computer.

If you checked and fixed anything there and still have issues then check your hardware from CONTROL PANEL / SYSTEM / HARDWARE.
Any exclamation marks by hardware need fixing before you investigate any further

USB flash drives can fail for no apparent reason.
Sandisk Cruzers are especially bad for this.

USB hard drives should be treated with extreme care.
This is a real hard drive ! and knocks and bumps can quite literally kill them.

It is possible to remove drives from the enclosures in most cases and connect directly inside a PC to fully check it.
You should also do this to cheack the drives connections are not bad inside the enclosure

Note that if you hear a drive clicking or pinging this could be the worst thing you would hear.
Known as "The Click Of Death"

If none of the above steps help look at updating the drivers from the manufacturers web site in the support section.

Nothing to do with the OS. First test it in another pc to make sure the problem is with the laptop and not with the drive -it might have just died. 
Some drives need  more power to function than an laptop usb jack can provide. Make sure it's plugged in with the auxiliary power supply.