I'm not sure there is a consensus on this. Depending on who you ask, you'll get different answers. My approach is to always use the correct spelling (such as management) on my sites so as not to make the user think I'm not professional enough to at least spell check my content.
In the case where there are multiple spellings for a given word (theater, theatre for example) I use the most common spelling for my target audience. So in the states I might use theater... but perhaps in England I might use theatre (assuming that is the most common spelling in that country).
If I were going to try to target uncommon or incorrect spellings of certain keywords on my site, I personally would dedicate a separate page to the other uncommon or incorrect spellings. That page would make it clear why the page existed and include an obvious link in that explanation to the page that has the correct spelling. But at the moment I don't even bother. I simply use correct or most popular spellings.
I've heard others say that they mix correct and incorrect spellings (which I personally think looks unprofessional) in their content. I've also heard of people putting the correct spelling on their site but using the meta keyword list to list the incorrect spellings (though this carries little if any weight w/ most of the SEs these days).
Also, Google does a pretty good job with their DID YOU MEAN #*$!#*$!#*$!XX hints to let the user know that they might have spelled the word incorrectly. So I don't lose a lot of sleep over it as far as my content and organic search.
Now PPC keywords are a different story. If we are targetting a particular keyword on a PPC campaign, we WILL include incorrect spellings in our keyword list for that ad. If someone clicks on the ad, they are taken to our site where the word is spelled correctly... and perhaps they will learn how to spell it for future searches. :)
[edited by: ZydoSEO at 11:28 pm (utc) on Dec. 29, 2007]
