This connector called and are they commonly used

Update:

As Passerby notes in a comment, the connector in your picture appears to be keyed. In which case it is not a generic 0.1" header connector. It may or may not have differing latching arrangements.

Original Answer:

What is the connector called

They are called header connectors, designed for (usually) 0.1 inch pitch connectors. They mate with header pins.

The housings come as singles or as strips of several combined, you can make up cables from parts or buy pre-assembled sets like these:

• 2-pin 0.1" spacing pig-tails
• 10-pin IDC Socket Rainbow Breakout Cable
• 6-conductor 0.1" socket-socket cable
• Female/Female Jumper Wires
• Female/Male 'Extension' Jumper Wires

The last two items are useful in that you can tear off a group of as many connectors as needed for a specific application. You can cut the cable in half to make a lead that can be soldered at one end.

The wires appear to be crimped into the connector somehow.

Usually the wire is crimped to a metal recaptacle and the assembly then is pushed into a housing that has a plastic latch to hold the assembly in place:

one side has a latching tang
use a knife to lift the retaining tang
like so
then the wire slides out of the housing

Is there a special tool I need to re-attach them?

No, just push them back together, so long as the plastic tang is pushed into it's original position, it will lock the metal receptacle in place.

You should be careful to have all the signal lines de-soldered before you try cutting the legs. If you don't you can easily tear up the signal traces when cutting away the legs. Use a small X-acto knife to lift up each leg of the signal lines while heating the connection with a soldering iron. Once you have all the signal pins lifted away from the contacts you can then cut the metal support legs, often with just a good pair of small diagonal cutters as the metal on these connectors is not that hard. I find that safer than using cutting wheels that can catch or break and end up damaging other areas of the PCB. I often save a damaged pair of diagonal cutters for such jobs as sometimes you may mar the blades on the cutters. If you have a nice pair of cutters and don't want to risk them, go buy a cheap pair for doing jobs like this. Once you have the legs cut you should be able to heat them up individually and pluck them from the holes.