What is the difference between "till" and "until"?
@RegDwight is correct in every particular. Till is indeed older and the two can be used pretty much interchangeably.
There is really only one usage I can think of where you would not use till: in setting up a negative conditional.
Until my landlord fixes the plumbing, I am not going to pay the rent.
I am not going to pay the rent until my landlord fixes the plumbing.
Here it would sound strange to use till, and I'm not really sure why. Perhaps it is the negative.
One more thing. Sometimes you will see people spell till as a contraction of until: that is, as 'til. This is simply wrong, and not seen outside of old poetry and modern greeting cards aiming for a "poetic" tone. Anywhere you see 'til being used, till would be the correct word.
Usage
According to the usage notes from the entry for till in dictionary.com, until and till are interchangeable:
Till and until are both old in the language and are interchangeable as both prepositions and conjunctions:
It rained till (or until ) nearly midnight.
The savannah remained brown and lifeless until (or till ) the rains began.
Till is not a shortened form of until and is not spelled 'till. 'Til is usually considered a spelling error, though widely used in advertising: Open 'til ten.
Etymology
According to the entries for till and until in the Online Etymology Dictionary, until would have derived from till:
until = und + till, where und was an Old English word meaning "as far as, up to".
till O.E. til (Northumbrian), from O.N. til from P.Gmc. *tilan (..) A common preposition in Scandinavian, probably originally the accusative case of a noun now lost except for Icelandic tili (..) the noun used to express aim, direction, purpose.
until c.1200, from O.N. und "as far as, up to" (related to O.E. end; see end) + till "until, up to" (see till). Originally also used of persons and places. Cf. Swed. intill, Dan. indtil. The Mod.Ger. equivalent, bis (O.H.G. biaz), is a similar compound, of O.H.G. bi "by, at, to" and zu "to
Frequency
Corpus of Contemporary American English:
until = 176K occurrences
till = 11K occurrences
British National Corpus:
until = 39K occurrences
till = 5K occurrences
It's been suggested that there's a difference in aspect: till is used with continuous actions, while until is used for perfective. However, this is not supported by any references or general usage, and seems to be an independent analysis.
The only difference is that until has no homophones. I'd suggest using until whenever there's a risk of confusion or difficulty in pronunciation, and only use till where it's suitable for the flow. Till, being older and ambiguous is often used poetically ("till death do us part") which affects the tone of the sentence. I therefore generally avoid till in technical writing.
Finally - as has already been mentioned - 'til is a hypercorrection, and is best avoided.