put more of those types of boxes and shelves on that wall and then put something in the box that hides the meter. I did this with a thermostat that was on the first wall you saw entering my old apartment.

I would place a opaque layer on the inside of the glass - can get them at home depot - it is a thin plastic sheet that makes the glass look like it has texture. Then go to the Container store and buy 2 more square boxes and hang them in a interesting pattern on top of this meter box. Place colorful vases or smth similar in the boxes that now act like shelves...

try to get dark wood boxes same as the one that covers the meter.

I'd place a bookcase or shelf around/under it so that it looks like a box sitting on a shelf. Then you could disguise it as a bookend, clock, picture frame, whatever.

Ok this may look sinister or insane , and I'm not sure it would match your decor , but I would maybe hang a mask on it : http://www.unitedmask.com/Masks/images/Paper%20Mache%20Animal%20Masks%202.JPG
In the Indian neighborhood here in NYC they have a very impressive selection of paper mache masks of various dieties maybe your town does too. Or you could make a paper mache deer head or something http://www.unitedmask.com/Masks/images/Paper%20Mache%20Animal%20Masks%202.JPG
If you want to be more normal I guess a larger more opaque kind of box/ shelf would be good, a flip top compartment for the meter is a good ideas - or put a floating shelf over it that you could use for books , a little altar - with hanging fabric to cover the meter- or a landing strip, since it seems to be by the door.

Sorry, deer head link here: http://www.apartmenttherapy.com/chicago/artwork/the-deerhead-project-by-jennifer-khoshbin-062713

I'd go with a set of bookshelves against that wall, with the meter sitting inside a shelf. Then put something on the shelf to hide the meter... a big colorful vase, some picture frames, etc. IKEA's Expedit shelves would be perfect for this: http://www.ikea.com/us/en/search/?query=expedit

Good luck! (I'm doing the same thing with an unattractive thermostat in my own home).

i would get an extra deep stretched canvas, something like this : http://www.artsuppliesonline.com/catalog.cfm?cata_id=8874 that is more proportionate to the wall and you can hang in a more normal place and still cover the meter. then get creative with the front. paint it, modge podge, whatever you want that goes with the rest of the rooms decor.

if you got the right canvas size i would even consider securing a full length mirror to it, just make sure that the nail/hanger is sturdy enough.

My electric meter is hidden by a wall-mounted kitchen cabinet. A hole was cut in the back to accommodate the meter and there's a bit of useful storage space inside.

As a DOUG (Dumb Old Utility Gal), I have to add the obligatory:
Make sure you comply with all utility safety requirements. They may have specific material or clearance limitations. If you don't have some sort of remote read technology (and it doesn't appear that you do) I'm assuming they have to come in and read the meter - so make sure it is still easy to access.

Actually, the more I think about this the more I am surprised the owners were allowed to keep the meter where it is during a conversion. I'm not conversant with DC utility tariffs and rules but I would expect that it would have to be relocated to meet code/comply with state regulatory/safety requirements.

I've been wondering how to cover a thermostat in my living room. These ideas are awesome. Thanks!

I agree with all those who have suggested you get some more boxes and create an interesting pattern with them on the wall.

i myself would paint the existing box white and put some nice fabric inside the glass pane to hide the meter.

here is an example of what i have in mind:
http://lovelydesign.blogspot.com/2009/02/fabric-backed-treasure-wall.html

I have an ugly thermostat in my apt. and to cover it I hung a pretty wooden fan that a relative got from China on a nail, and voila, it's out of sight, and to access the thermostat you just swing the fan to the side. Free, and no construction of boxes required!

Quick fix:

Paint the box in the same colour as the wall, or perhaps white like the door.

Put a photograph, post card, small picture or similar behind the glass.

Place a small, decorative object on top of the box. A bowl for change and keys, a small plant, alarm clock...

How about a large leaning floor mirror like the Ikea Hovet?

I know this is going to sound a lot different than most of the advice, and I know that because I am young and in love with all things quirk....but what about framing it out like a clock face, as opposed to covering it up with a box? With a few other clocks hung in random (and utterly impractical) places on the wall mixed in with some art pieces, it might be sort of cute and kitschy.

That is, if you like kitsch :P

How about using the window, if the frame opens for reading the meter, as a picture frame. If you want you can use the wall as a gallery. Perhaps adding a shadow box for collectibles.

Just me, I like the box as is. There's something wickedly quirky about that meter. It's there, it's utilitarian, get used to it! I'm unabashed about lamp cords, pipes, radiators etc. I guess coming from NYC, that can't be helped. Hey until everything is wireless, this is our fate.

Depending on your style, you could get away with keeping the meter visible and adding other gadgets, gears, trinkets, dials and such and doing some sort of "steampunk" styled art piece there.