You can hang curtain rods or screens from the ceiling! That's what I did in my condo. Just make sure you get the proper drywall screws that will anchor them

The first thing that comes to mind is IKEA panel curtains. They are one of the few things that will cover the window, without eliminating the whole window alcove in the living area.

An attractive roman type shade is mounted inside the window sill, I believe, so something like that might not be a problem. Although that doesn't help if you want the look of curtains, in that case hanging from the ceiling is probably a good solution or just flanking the windows.

If you are wanting to hang drapery, I'd suggest a track style system like Umbra's glide track, or IKEA's KVARTEL. Both of these can be ceiling mounted without a gap at the top the way a traditional rod would have when mounted from the ceiling.

Many bay window rods can be installed on the ceiling instead of the wall. For example, look at Antique Drapery Rod.
You could also use a ceiling mounted curved track, which is shown here: http://www.easycurtainideas.com/curved-curtain-rods.html

You could also install shades at the bottom of the window that I have seen and you pull them up to where you want them. It is great because you still get lots of sunlight by just pulling up halfway. It would be lovely to get them in a striking color!

A box valance might work, but it'll be tricky in those bays.

If you want curtains get the the ones that go on a track. I personnally don't like drapes or curtains, they really aren't nessary and are dust and allergy collectors. If not, buy some of those shades that that raise and fall from the top or the bottom, it gives lots of control for privicey and you can get them with blackout if need be. I like just haveing the top come down, lets in all the light without looking at neighbors or them looking at you.

There's always Roman shades - or perhaps (since light is really important to me in my living space) take a page out of Brooklyn Limestone's books and do some type of half window treatment -- http://www.brooklynlimestone.com/2009_06_01_archive.html

On another hand, if you're more of a traditional/maximal type, I could see an interesting textile pelmet / cornice across all three windows in the bay with drapes on the sides working well. Either going very simple with a graphic striped edge, or tipping towards more opulent with a chinoiserie inspired fabric maybe... I lean towards maximalism myself, which I know isn't everyone's taste. But something like perhaps-- http://gallery.apartmenttherapy.com/photo/jason-jon-new-york-house-ii/item/117003

Since it looks like you have popcorn ceilings, I would be super careful about hanging anything from the ceiling as it will permanently leave a mark you won't be able to hide without respraying the ceiling. I would try to find fixtures that mount inside the window frame.

We did a half window treatment in our kitchen which is a plastic ceiling light cover in a frame, easy enough if you're handy. http://i288.photobucket.com/albums/ll196/rainarana/windowscreen.jpg Something similar might work in the bedrooms if you wanted the option of letting in light but retaining privacy. You could also mount curtain rods outside the windows. For the bay you could go for a rail at the top, as has been suggested. Depending on what can be mounted and what kind of style you plan on decorating, I really like the roller blinds we have in our living room, http://www.blindsgalore.com/WindowProduct.asp?id=709406 (they come in different colors, with/out print.) I wouldn't think it would be a problem mounting them if blinds can be done there.

For the bay windows I'd run a side-swept curtain between the big flat walls so that it separates the bay window area from the rest of the room. I'm thinking it would be tied back and draped like those curtains that always frame Baroque paintings, only made of crisp white linen.

I'm super-jealous, by the way.

Okay, I'm not sure if that made any sense. I'm suggesting you treat the bay area as if it were part of the flat continuous line of that living room wall, hanging the curtains from the ceiling. Doing so would create a pocket behind where the curtain is hung.

I vote for the bay window seat pictured in the middle of this article: http://freshome.com/2011/11/29/36-cozy-window-seats-and-bay-windows-with-a-view/

In addition to window treatments - I think that "grounding" the windows by putting a chest or some other case-piece under the windows will balance out the proportions of the windows being so close to the ceiling.

Both sets of windows would work with curtains on a track mounted on the ceiling. IKEA has the simple Kvartal system... install one for a thick curtain or two for a thick curtain in front of sheers.

For the first bank of windows, though, you could go for roman shades that pick up some key color in your room. If you're on a budget and are fortunate enough for those windows to be a stock size, you can get roman shades for a song at J.C. Penney. We covered 8 windows with really lovely shades in a great color for only $130.

If your windows are not a stock size, you can get somewhat affordable custom shades through etsy.com or sometimes your local tailor.

I saw an idea a decade or so back by Mary Gilliatt (Decorating on the Cheap) about using roller blinds upside down. The blinds were installed low on the window and then pulled up for privacy. A pulley or screw-eye hook was used at the top for the cord.

I would consider plantation shutters. They mount on the inside of the window frames. They don't "soften" a window the way curtains do, but they give privacy and light control.

A lot depends on your personal taste, climate, and other missing details.

If it were MY house, I'd get a double rod arrangement for the bay and hang sheers floor to ceiling with more opaque drapes at least on the outer edges, perhaps for each individual window (meaning when opened, the opaques would bunch on the outer edges and the inner corners.)

I actually have similar windows in my bedroom as the one in yours. I like a very bright room n the daytime, so I have a double rod with sheers and with white Dupioni silk side panels (that do not close). Between the Dupioni panels (purchased on a clearance sale, thus not enough panels to completely cover the window) I hung a pair IKEA curtains http://www.ikea.com/us/en/catalog/products/60173861/ to fill out the rod and obscure things so the neighbors can't see in.

Works for me. Might or might not for you!

Maybe you could get to know your neighbours by putting a note through their door explaining your window dilemma, and asking what they have done for their windows. They might invite you in for a friendly cup of tea and a tour of their place (many people just love showing their homes).

This isn't directly related to the drapes question, but someone above mentioned "grounding" the windows and thus elongating them -- I can't remember where I saw it, but a designer with similar windows built out windowsills/almost a small windowseat, and then installed mirrored paneling beneath each window. It gave the windows the appearance of reaching from floor to ceiling, which was lovely. Depending on how you feeling about privacy, you might get away with no drapes at all if you did something like this in the living room (probably not so important for the bedroom).

Your windows are virtually the same as the ones in my condo. I love the additional space that they add to the rooms and the views are better than a flat window provides. These windows are to be celebrated, not viewed as difficult! Nearly everyone in the building has what we refer to as plantation shutters. Yes, they are expensive but add to the overall value much more than a fabric treatment. They take up less visual space, allow for light control and are pretty neutral in style. I've owned both the solid poly type and the wooden ones. They both look great and perform well - go with the widest width that you can afford and be mindful of how the framing is done - you want to maximize the light.

Follow up - don't obsess about filling in every darn space in your place! I have a short backless bench sitting in one of my window alcoves - it adds style (you can drape a throw across it for color) and is light enough for me to move for use as extra seating or a footstool. A small writing table and chair works but does make it more difficult to enjoy the view - maybe a standing desk or a pub height desk? Others have cozied up a chair/table/lamp in these alcoves. Built ins are very classy, but expensive and permanently define that space.

I like the idea of some sort of blinds in the window for light control, be they tilting slat ones (I like these in the living areas for controling light) or honeycomb or other pleated ones in the bedroom for complete privacy and light control, and I like the top down, bottom option on these to let a little light or air in at the top while the rest of the window is covered in the bedrooms.

Now, from light control onto style. I think these windows all need to be elongated by having curtain panels to the floor hung on either side - not to cover hardly any of the window glass, but mostly next to the windows. They don't need to close (you have the blinds you need for light control) they are just there to look good and anchor the windows on the wall.

I'm not big on pelmets or cornices at all, but I don't like the way the window meets the ceiling, so I would think about a simple, not very long, just a few inches really, up to say 6 or 7 inches max, valance, that is not hardly gathered at all. I made one for a window valance - it is just a few inches wides than the space, so only gathered a tiny bit to give the piece some fullness and not look like a flat piece of fabric. Looks very tailored, not flouncy like gathered valances. Is on a spring rod at the top of a window over mini slat blinds. You may get the same finished top effect if you choose a blind with a finished top, deeper than the 1 inch kind of headrail, one that gives the definite sense of a finished top, a separation between the ceiling and the window/wall.

Also think wood chests, tallish approaching window height, best below windows. I don't like the picture with seating directly under this window at all - doesn't feel like it would be a cozy place to sit with the window so high above it.

my first thought had nothing to do with drapes or coving the windows up! If the funds allow it, for this alcove, I'd get some custom built-ins and either turn it into a bench or bring them up higher toward the windows even. I do like the idea of the plantation shutters - I've never been into curtains or drapes, I think that they just look heavy. Not sure about the bedroom, I'd have to see it staged with the rest of the furniture. Good Luck!