Absolute zero is defined as zero degrees Kelvin. The closest recorded temperature to absolute zero that I could find is 0.0001K, for helium gas.

Your question about what would happen to an object cooled to absolute zero is a great one! All molecules are constantly in motion (the bonds between atoms are vibrating and changing shape). The speed of this motion is dependent on the temperature of the molecule. As you can probably guess, motion is faster at higher temperatures. Changes in molecule motion with temperature are responsible for phase changes.

Water vaporizes at high temperatures because as the water molecules move faster they bump into one another more often, pushing each other away and taking up more and more space, eventually forming a gas (steam).

Water freezes at low temperatures because as the water molecules slow down they coalesce, or come together like pieces in a puzzle to form a crystal- like matrix. (Why is ice LESS dense than water, then? If the molecules are moving slower, they should be closer together, right? Ice is less dense than water -- it floats.)

Even when water freezes, the molecules are still vibrating. Only at absolute zero do molecules stop moving completely. What sort of phase change would this cause? According to Einstein, who based his work on an Indian physicist Satyendra Nath Bose, this would result in a completely new form of matter.

Albert Einstein speculated that when molecules stop moving, the atoms would fall together and merge into one atom. The individual atoms (oxygen and hydrogen, in the case of water) would loose their identities and form what Einstein called a "superatom" or what we now call a Bose-Einstein Condensate.

Last year, Carl E. Wieman at the University of Colorado in Boulder won the Nobel prize for his work on Bose-Einstein Condensates.

The closest to absolute zero anyone has reached is around 150 nano Kelvin. The group ended up receiving the 1997 Nobel Prize in Physics for it. They got the prize because they ended up proving a theory called Bose-Einstein Condensation which had been made decades before it was proven.

They achieved the cooling by taking already cold vapor of atoms, (3K 87Rb atoms) and slowing them down further with a 3 dimensional laser setup. If you want more detail your welcome to look at this link here

For the really good stuff, look up Steven Chu on the web. He has some good educational equipment hiding somewhere. A quick explanation of Bose-Einstein Condensation (or BEC) is that due to quantum mechanics, there is a limit on how well you can know the product of a particles momentum and position at the same time. This theorem is called the uncertainty principle. So if you know exactly what the velocity of a particle is, you can't know its position exactly no matter how good your equipment is. You do however know a region that the particle could exist. If you had a billion particles, each with the same velocity, each time you looked you would find the particle in a different place.

So what Einstein theorized was that if you could slow down an atom enough, due to quantum mechanics the atom size would spread out. If you kept slowing the atom down, it could overlap with other atoms. That is exactly what happened, the atoms ended up spreading out enough that the atoms existed as a single entity, rather than a collection of separate atoms.

PS. An interesting fact:
The navy funded the research. What the grant proposal promised was the possibility of the most accurate clock in the world. As far as I know no one intends to ever build the clock.

The record for the coldest temperature which has ever been reached depends upon what you kind of substance you are interested in. The coldest temperature which a solid object has been cooled to is about 60 microKelvin, or 60 one-millionths of a degree above absolute zero. Certain gases have been cooled to about one nanoKelvin, or about one one-billionth of a degree above absolute zero.

However, this temperature can't be maintained indefinitely because the gas slowly solidifies, and warms up when it does so. In a certain kind of machine called a "nuclear demagnetization refrigerator", it is possible to take a piece of copper and cool only the atomic nuclei to temperatures of roughly 1/4 of a nanoKelvin. This is kind of an unusual situation though, where the nuclei of all the atoms are very cold, but the electrons of the atoms are much warmer. You can read some more about nuclear demagnetization refrigerators at here and some about the very cold gases at this link I don't know what would happen to a substance if it were cooled to absolute zero. Certainly very many changes happen to it on the way to absolute zero.

If you think of water for example, it changes from steam at high temperatures to liquid water as it cools. When it gets still colder it becomes ice, which is a solid. These changes are examples of phase transitions, in which a substance changes its properties dramatically as the temperature changes. Some substances (like the element dysprosium) become magnetic when they get colder; others become liquids that flow without any friction at all (like helium); still others allow electrical current to flow through them without any resistance (like aluminum).

Mostly these changes take place because as the substance gets colder, the vibrations of the atoms in the substance become weaker and weaker. At absolute zero the vibrations nearly stop all together - the only vibrations left are called the "zero-point motion", but they can't produce any warmth.

I'm not sure what the current record is, but I believe it's around a few billionths of a degree above absolute zero. For reference, the coldest parts of space appear to be about 3 Kelvin! As you approach absolute zero, atoms and molecules lose their energy and slow down. At absolute zero, atoms and molecules in a system would be in their lowest possible energy state. However, according to the Third Law of Thermodynamics, it is not possible to bring a system down to absolute zero.

However, even though absolute zero cannot be achieved, dramatic changes in the physical properties of matter (such as Bose-Einstein condensation and superconductivity) can emerge at temperatures near absolute zero.