What is the special equipment that is used to measure resistance of a wire??

An OHM Meter..

Some advice stay away from Radio Shack, 'Radio Crap', when you decide to buy your meter.....after all the invented the TRS80 computer generally refered to as the 'Trash 80'
They always blow up if you are on the wrong setting...like trying to measure 120 v and the meter set on Ohms.....
Cheap and no protection...fuses

Wire resistance usually are very small which cannot be measured by an ordinary Ohmmeter. There is a special but similar equipment that is sensitive enough to measure resistance in micro ohm unit. It is called; 'Wheatstone Bridge'.

Ohms are the unit of measure, an Ohmmeter conducts the measurement...
A "Multimeter" or "VOM" has the ability to perform as an Ohmmeter..

it is called an OHM meter

an ohmmeter, but sice you are going to get 100% of this as your answer , i am going to make my own ...it is called resistance-of-wire-o-meter.

Uhh, yeah, just a multimeter or an ohmmeter. If you are talking about resistivity, then you probably need some more equipment.

Yep, a multi meter which looks like...
http://www.radioshack.com/product/index.jsp?productId=2103534&cp=&origkw=ohm+meter&kw=ohm+meter&parentPage=search

There is a special setting on it for ohms, but it can also measure current and voltage as well which is pretty handy.

An ohm-meter or a multi-meter