I'm seeing two moderately sized pieces of art, probably by the same artist, something like pen-and-ink drawings or charcoals, in very plain frames -- one on each wall, hung level.

I agree. Or if you moved the couch over a smidge, you could put a nice standing lamp there.

You could also use some curtains.

Maybe an interesting lighting fixture mounted on the ceiling?

Can you show us a little bit more of the room? Some context would help!

Um... I'm perplexed. For one thing, that's hardly an empty corner; you've got a couch wedged in there! Secondly, wouldn't it go against your "minimalist" theme to do something decorative just for the sake of doing something decorative? If the rest of your apartment is as spartan as you suggest, I think it would be rather odd to have this one corner spruced up with objets.

What about something like this? It's light and airy and brings a little of the outdoors indoors. It's also not the intrusive to the minimalist decor.

http://www.eurofase.com/productlarge.asp?CATNUM=&STATUS=ACT&MODEL=12317

emmalazarus, we don't all need curtains. We prefer the minimalist look, too.

I like the idea of a standing lamp or a wall mounted fixture.

Maybe a can light in the corner. CB2 sells them for $20 each. If you put a large tropical type plant in the corner also, the light will cast nice shadows on the wall/ceiling.

Touchy touchy! Sorry but don't you find basic white Venetian blinds an eyesore? Even some nice white paper blinds would work or some simple gauze curtains would stick with the minimalist theme.

Its hard to say what the rest of the room looks like, but that corner does look pretty full to me, even if the furniture and existing accessories are sleek and minimalist. I would add something softer at the windows, probably just fabric shades since the sofa is passing in front of one of the windows. I can't tell what the wall color is, but maybe a soft white in the style of a classic roman shade (like these: http://www.smithandnoble.com/sn/product_detail.jsp?prod_oid=251291&nav_cat=-17993&sch_cat=Classic%20Roman%20Fabric%20Shades&view=swatch)
or for a little warmth (even though I know its very done, but it's classic) some bamboo, or matchstick blinds, in a light color like these:http://www.pearlriver.com/v2/FramesCat.asp?iGroup=303
Then add some framed artwork, maybe 3 small prints in a vertical stack on one side of the corner only, I would do it above the back of the sofa...If there is room on the other end of the sofa I would also free the sofa from the corner by just a few inches to give it a little breathing room...then add just a few brightly patterned trendyesque throw pillows, (ive been eyeing the new patterns from thomas paul) 3 maybe with at least one pillow being on the smaller size that draw in some colors from the art.
You could also add a single sheer curtain panel to the window that is free from the sofa, something in acolor close to the wall color, to keep it very simple and neutral, and then swag it back with just a simple grossgrain ribbon even.

I think light would be good. I think an uplight with a simple shade or maybe some natural elements.

It belatedly occurs to me that we're seeing a prime example of a cool person in the sense Maxwell defines in the book. I'm not one of the curtain brigade (since I mostly hate all curtains except simple panels to the floor), but the curtain faction, the light faction, the art faction, and the plant faction -- we're all after the same fundamental point, which is that the apartment (in this corner) looks very low on Heart.

All together now: You've gotta have heart!

...minimalist? It's a nice architectural feature. With a whole 2 feet either side? Plus a commanding urban view? This corner is breathing space. Clean it up and put nothing there. Well, maybe a spot/floor light pointing upward (dimmer, of course). Let the eye travel to the outside.
Otherwise any future plans for drapery panels to frame your windows and soften your minimalist look?

Unless the couch fits snugly on both sides, like a built-in, then the couch is too close to the corner wall. As is, anything that protrudes from the corner wall or ceiling would make that corner more claustrophobic.

can we see another pic of the space? a different angle? that might help.

How about a pot on the floor, filled with rocks, with bamboo shoots? Put it underneath a very simple hanging lamp and it'll cast interesting shadows and create a reading area. It would also bring in some color without being overwhelming and stick with the clean lines of the room's furniture.

how about a nice tall vasse with some curly willow or bamboo sticks in it?

Well, if you want something kind of different, how about curtain on a hospital rod (the kind of track at the ceiling, which, would curve in the corner), which, when full-out would cover both windows AND the corner part of the wall, but which, when open, would "bank" in the corner.

Plus... you could place the sofa a cata-cornered angle and THEN you could still put something in that corner or not, like a plant (either a real one, which might catch light from both windows, or fake) and/or an up-light can-light thing to wash the curtain and/or plant.

PLANTS. How about a small tree on a stand, or a tiered plant shelf? I think plants add lushness to minimalism (unless you create a jungle, or course.)

i'd like something funky and original while keeping my minimalist, neutral scheme.

those two idea clash. as stated previous.

you should not do something for the sake of it.

however, i would suggest one single bright colour to make you notice your "neutral" scheme. like a bright lemon-green. or lite high sugar pink.

I will second the suggestion made by Curtis.

Maybe paint one of the walls an accent color...it doesn't have to be bright or bold necessarily, but it would make the corner look less naked. And, I like the idea of different blinds...perhaps in a tone that picks up the throw.