We have similar cabinets for stain color but had them stained a bit darker. We opted for an off white in our living area. A light gray (on the warmer side) or a cream (not yellow-ish) could also work.

I'd paint it the same color as the trim in the adjacent rooms.

I would suggest removing the built-ins because I don't think they'll enhance the look of the space even if painted or re-stained.

I agree with Elle, I'd remove them. They are going to impede upon your overall room layout, and look a little awkward in the current location.

Keep them - if your style is traditional they add character and style. For the update - one simple step is new hardware. That is a useful step.

You have stained wood base and window sill, so what you do next should be comprehensive. You can wrap foamboard in fabric or wallpaper and add color to the back of the open shelves. A contrasting tone in your accent shade or just a tone of the wall color could be nice there.

The main thing is what you put on the shelves. If this is your living room, do you or your husband collect anything personal that would be great displayed across the shelves combined with books? Sculptural items can be great. If this is a room that wants a television, you could remove some shelves and mount the television in the upper box area on a swing arm mount and use the closed storage for components . . there is a remote sensor you can buy to do that easily.

Yes, you could paint this a deep shade, but then you would need to paint the rest of the trim. Yes, you could use a product like polyshades to deepen the wood tone, but again, you would want to carry that through. Due to the ornate mouldings on all the painted wainscot in the entry and formal dining area, I'd be inclined to do a soft warm gray here on the walls . something like bm edgecomb gray (great against this - nice rich but not red or gold wood tone) .. and go more dramatic with painted wainscot in the other two spaces .. maybe bm river gorge gray on the wainscot in the dining room with edgecomb gray above . .. use edgecomb gray on both the upper and lower walls, doors and door trim to give the entry a sort of modern traditional feeling with all the same sheens . .and tones .. this would make the rooms flow well .

http://www.benjaminmoore.com/en-us/paint-color/rivergorgegray

http://www.benjaminmoore.com/en-us/paint-color/senoragray

http://www.benjaminmoore.com/en-us/paint-color/edgecombgray

what that could do is present a range of tonal colors from off white that span across light and true mid tones to help balance in the next room the deeper wood tones in your cabinet . . you may be able to repeat those wood tones in an open armchair across the living room ..

Some of the shelves look a bit bowed. Is hubs willing to replace those? Is there something you've always wanted to collect? Barter investing in your personal collection for keeping the built-ins.

Agree with deco, I would be concerned about the shelves not being even, and wonder if at that width and no support midway, if they could hold anything of any weight without additional bowing. I love a good built in, love shelves filled with books and additional storage, but this particular unit, given the shape it is in and the location, does not seem worth keeping.

I'd paint them the trim color! I love them, look very useful!

I would get some bamboo shades for the window to match them and leave them how they are. But then I like my colors to contrast.