You can speak off the top of your head, or you can look it up. In the US, and I suspect this mirrors most other jurisdictions, 17 USC Section 120.

Note that this "photographer's exception," as it's sometimes called, does not apply only to the taking of a photograph, but to the distribution or public display of the photograph, which would allow such things as use on a book cover.

It's a dicier question when it comes to public art, such as a sculpture, and I don't know the answer for sure, but I suspect that the answer is that it's okay if the art is included in the scene you are photographing, but not okay if the photograph is primarily about showing the art work. (I just noticed Wintaka's link, which apparently answers the question, at least for the UK, by indicating that it's not an infringement to draw or photograph public art. The US statute, by contrast, refers only to buildings, not to art. Still, without looking it up and nailing it down, I would be shocked if it were illegal to take and sell a picture of a public square because you can make out on a single corner a small statue that is under copyright, or if there were a billboard in the background with copyrighted advertising text, or someone wrote and owns the copyright to graffiti painted onto the side of a subway car that happens to be passing by.).

If you use the painting to make the cover of your book and as such it helps to sell your book, you are using someone else's work for profit without their permission. If you take a picture of the painting and use it as your Christmas card - just sending it to friends and family - it would not be of much note (though you should still give credit)
The artist owns the work, it is copyrighted even if a copyright was never applied for. You need to contact the artist and get permission. I would bet you any money she/he will be thrilled (unless of course they have gone on to do much more and better work and do not want that painting out there to represent them) Like if someone took an old poem of yours that you had just sent them and never intended to publish but they put it on their blog and attributed it to you but it is so not what you now do and you never intended it to see the light of day.
It's complicated, but bottom line is you need to ask the artist. It's the right thing to do.

Museum's rights
 

I am curious about Bill Lantry's claim early in this thread that "museums get to say no, even if the artist says yes".
This is surely incorrect, unless the artist has specifically transferred copyright to the museum.
Museums and galleries like to maintain they have copyright over their holdings (they make plenty of money from selling reproductions) but they do not. It is important to stand up to them on this issue.
PM

You're right, Philip, that assertion was incorrect. Although I imagine that if a museum owned the only copy of a painting, even though it didn't own the copyright it could legally prevent the artist from having the access needed to make a proper photograph of it. So if the museum owned the only copy and there had never before been a proper photograph of the painting, the museum could "say no" and perhaps have bargaining power as a result.

There was an interesting case a few years ago with the movie 'Basquiat' about the life and work of the eponymous graffiti artist. The director was denied permission by Basquiat's estate to feature any original paintings, even ones that he personally owned!

A recent, relevant case in point:

http://www.telegraph.co.uk/culture/a...-painting.html

I'm not sure how on point that is, Ann, but it's quite interesting. It's weird to think that the value of the painting is almost entirely dependent on whether or not it is accompanied by a legal certificate. It's the exact same painting with or without the certificate, and yet it's worth a fortune with it and almost nothing without it. So any notion that the financial value of the painting inheres in its beauty or craftsmanship flies out the window. Crazy.

Ann,
Having stumbled onto this thread a little late, I just wanted to add something to what Nemo said about high resolution image- a professional artist with some degree of reputation might want to be involved in the proofing, not just for resolution, also for color, and not just involved, but should require right of final approval of the quality of the reproduction.

Nemo?.....

My bad, I was channeling Mr Hill at the time. What can I say I'm in love. I meant Rick.