I have a feeling this might be a British vs. American English thing. As an American, "ill" or "unwell" feels ... just a little ... too elegant a way. They basically mean the same thing, but sick is, again at least in American English much more common and useful in everyday speech. I watch a lot of Brit coms, though (british comedies), and I notice that they use ill more than we do.

Ill and sick mean the same thing in formal language. Robert, the previous poster has 'hit the nail on the head'. As an Australian, ill and sick are used interchangeably and it depends on the speaker. In informal English, especially with the youth, ill and sick can be used as slang for something that is exciting/excellent/admirable. For instance, Felix Baumgartner's stratosphere jump would be considered ill or sick when used in slang.

And here's a British perspective: In GB English, 'ill' is the opposite of 'well'. If you don't feel well and can't go to work, for example, you would say that you 'feel ill'. 'Sick' has a more specific meaning: if you 'feel sick', this means that you are nauseous and feel like you need to vomit. If you say 'I was ill', we'd understand that you weren't well, whereas if you said 'I was sick' we'd understand that you vomited. The exception is when the adjective comes before the noun, for example 'a sick child' or 'her sick husband'. In this case, 'sick' means not well, as it does in US English. It also has this same meaning in certain phrases, such as 'a sick day' 'to be off sick' or to get a 'sick note' from the doctor. By the way, usually when this question comes up, American members make the distinction between being sick ( a minor illness such as a cold or flu) and being ill ( a more serious long-term illness or condition). This doesn't apply in British English, but I believe this to be the case in US English.

Ill is generally used related to a sickness, while sick has sometimes also a shade of feeling disgusted ("You make me sick!") or morally deviant ("Eww, that's sick, I can't believe you ran over that cat intentionally!"). Or cool, as Matthew pointed out. Although even 'ill' sometimes denotes an element of being bad in a conceptual way, as in 'an ill-conceived plan"