"IANAL" (I am not a lawyer) ... but ... I am working on some celebrity portraits and I have studied the issue a lot over a couple years. There are numerous different laws that apply - copyright, trademark, privacy, and right of publicity - and the they differ from country to country and even state to state. Be VERY careful if you live in California. It does not matter if the celebrity is living or dead. Their estate has the right to their image.
Now as I understand it - you can do a painting for your own use, even for a "fan site" on the Internet without permission from the celebrity. I am not sure about for use in a portfolio or samples you mail to prospective clients (I am still working on the legal issues surrounding my own) - however I recently spoke to the lawyer for a famous (late) celebrity, and he said he'd have no problem with that. What he'd have a problem with and others would not - is impossible to say. I cannot find any case law on that.
As I understand the law, you may sell portraits and cartoons to magazines, for editorial illustrations, without permissions (though it may still be recommended to get those permissions if you can - but that is the magazine's responsibility, not yours - I would write that responsibility into my contracts too).
You DO need permission from the original photographer to do so, however
. You may "get away" without getting that permission - by making the painting so different the photographer does not recognize their work. But there are also archives of portraits available where you can purchase such images (Associated Press Etc). Paparazzi will sell licenses to artists to use their photos. I would not assume all these other artists did not get permissions just because they don't credit photographers. That may well be the case - but do you want to take the risk? I know of one photographer getting a significant settlement when one of his photos was used without permission.
What you cannot do - under any circumstances is a poster, calendar, card, t-shirt etc with the image of a celebrity without their permission. You cannot use it in advertising (not even as parody).
These are all generalizations of course. There are many people flouting the law and getting away with it. I don't recommend that.