Is there geological evidence that the moon once collided with the Earth?
Is there geological (or other physical) evidence here on Earth that confirms the moon once collided with the Earth?


No, there isn't. This is, however, plenty of evidence that the moon formed due to a collision of a third body (sometimes referred to as Theia) with the Earth, and the moon formed from the ring of debris that resulted from the collision. 

This theory is often known as the Giant Impact Hypothesis and searching for this term may help you find other links and references elsewhere.


  If so what is that evidence?


To summarise the geological evidence, much of it is indirect evidence, in that it compares geology on the Moon with similar geology or features on the Earth, and draws conclusions to explain the similarities (or discrepancies).

Because of the sheer size of the proposed impact, it would have likely reconfigured the surfaces of both bodies entirely, and so finding direct physical evidence on the Earth would be extremely unlikely. (e.g. a massive hidden crater would simply no longer exist)

Geological Evidence


Moon rocks collected from the Apollo missions that have almost identical oxygen isotope ratios to similar rocks found on Earth of the same age.
A large portion of the Lunar crust is made up of Anorthosite, which is indicative of a large melting event. (with the energy for this supplied from the impact)
Zinc. Lunar rocks contain less zinc, but with heavier isotopes of Zn than those found on Earth, which by contrast has lighter isotopes in greater abundance. This is consistent with zinc being depleted from the moon by evaporation, such as during a massive impact event.
Density and volatiles. The Moon is 25% less dense than the uncompressed density of Earth. It is severely depleted in volatiles, with practically no water and less than half the potassium abundance that Earth has. The combination of low density and lack of volatiles implies that the Moon was not a simple accretion of early solar system material, but resembles the Earth's mantle in bulk composition. Volatile material would have been vapourised by the impact. 
The bulk composition of the Moon's crust. (This one does not actually involve the Earth, but I feel it is still important to mention.) The Moon's mantle and crust chemical composition could be explained if the Moon had a large iron core, but its core is actually quite small.


Other Physical Evidence


The ratio of the Earth and Moon's mass far exceeds any other planet in the solar system, and this begs the question of how did so much material become in orbit of the Earth. (Not evidence as such, but raises the question in the first place)
Getting more indirect...there are bands of warm silica-rich dust orbiting nearby stars which is interpreted as planet-sized bodies having collided with each other, so there is precedent for similar events happening elsewhere in the galaxy. (Again, I realise this is one is not strictly answering the question, but Earth Scientists often have to look well outside the Earth to answer their questions!)


Hope this gets you started!

Update:
I recently came across this short article, which provides a summary of some of the latest thinking on the Moon's formation, including the Giant Impact Hypothesis.

Sources: de Pater and Lissauer (2010): Planetary Sciences; Canup and Asphaug (2001), Nature