It's called a cantilever bump out. Very popular with the Prairie school of architects (Frank Lloyd Wright et al). Also commonly used in mid-century modern and mid-century split-level styles. You will see more decorative bump outs in in bay and bow window forms that also cantilever on older homes, but the cantilever area on the exterior is usually covered by the porch, or in a second-story application, there would be decorative trusses underneath.
Take a look at some of the prairie style houses, and you will see how these work.

I'm afraid I will have to disagree with fori on this one. A cantilever bump out only looks "cheap" if it is done to a house that doesn't fit with the architectural style of a cantilever. Generally, a cantilever bump should not be more than 4 feet at most because it can't be properly supported.

Our mid-century house has a cantilever, and it looks just right -- but the house has some strong horizontal lines and has a lot in common with the architecture found in Craftsman or prairie style houses.

I didn't mean to say they all look bad--I meant to say the ones that are done because they are the cheaper alternative tend to look like the cheaper alternative. To make them look like they aren't tacked on for most homes requires spending enough so that they don't look like they were tacked on. Except in some circumstances, the roof needs to be integrated with the existing roof somehow to look right, but often they are left with their own slope that doesn't go with anything.

Pretty sure if F.L.Wright did any afterbuild bumpouts, they didn't LOOK like afterbuilt bumpouts!

But SR is right of course, do it properly and it can look appropriate. Maybe I just haven't noticed the ones that look good, but I've seen plenty that don't!

This is EXACTLY what we are in the midst of, and no, the costs aren't anywhere near that low. This is our diningroom wall. The plan was to bump out 24", using 18" of the depth for built-in wall to ceiling cabinetry, with a granite topped buffet under the window in the center. This would allow us to do away with a bulky china cabinet and make the very small diningroom function a lot better.

To make a long story short, we are in California, and in order to get permits, a structural engineer had to be consulted. This added 2 months to the project and several thousand dollars. The builder was required to use steel 'strong walls' and hurricane straps, bolted every inch along the back of my house. And of course we needed a foundation.

So, what 3 companies bid on as a reasonably priced solution to our storage and space problem became a lot more complicated and expensive than anticipated.

On a positive note, I know where I am standing the next time the Bay Area has an earthquake. And, It will be gorgeous when it is competed.

fori -- F.L. Wright did do afterbuild remodels.
tamjo44 -- You just confirmed my fear about doing a bump out in CA (we're in So. Cal). So much for my luxurious master bath! I guess I'll just have to scale back my ambitions. :-)

mahlgold - we just did this in our bay window - if you remember my *lovely* before pics in my online album, the bay was a true bay, being just a window attached to the house. We bumped out the walls around/beneath it to create the space for the window seat that you saw in the after pics. Essentially, we needed a couple of footings and then they just built the new exterior walls, bracketed them to the joists (which did already run the way they needed), and extended the floor. Obviously, we did not need to do anything at roof level since the bay window was already in place. Our line item cost to do this was $5400. We're in MA and don't have the hurricane codes like others but our town is very strict w/ its building codes. Don't know if that helps but it'll give you a ballpark to start. - Kristin

We did a bump-out for a windowseat. It is a terrific way to get more, sometimes critically needed, square feet at relatively little cost. Inside and outside, they can also add interest to a flat box, and the casual irregular style of many cottages, like ours, lends itself nicely to a bump dropped on here or there.

As Fori said, though, they can be goofed up. A neighbor once added one rectangular bay to the front of a symmetrical cape. Even a nice veiling of shrubs and trees couldn't have fixed that one.