It doesn't look like you have a coffee table yet, so maybe something oval shaped to bring in some curves. Also look for softer lines in some artwork, and maybe some curvy candle holders and vases. A poof could be a fun addition that would give you the soft texture and shape as well as providing extra seating or surface space. Also table lamps: possibly go with a gourd shape and not something too angular.

Round things. Too many straight lines gives the space a harsh feeling. Round pillows, round tables, round rugs, etc. Fabrics with squiggly patterns rather than zig zags.

Try to play with texture too. Doesn't have to be ruffles, could be a flokati rug or a soft throw for the couch.

I'd head for a pattern and/or color (perhaps something that works w/your rug) in the drapes - the grey doesn't seem to help w/softening the angular furniture.

The two things missing from your board are the things that could make the difference, Lighting and artwork. Your throw, rug and pillows add softness and pattern, but all the larger pieces are straight lined and boxy. I'd suggest table lamps with curvy hammered brass bases, and artworks with rusts, browns, and golds in soft swirling organic shapes to pull out the colors from the rug and pillows and balance the clean lines with some curves.

I'd change the drapes and the rug ,d bring. Lighter and warmer tones like coral or yellow and bring in an oval or round glass/ stone top metal coffee table and bring in color with accessories go on the shelves.

I'd find/make some accessories in the red color from the rug. Some candles/vases/frames could be interesting against the neutrals. Maybe pots for your plants in colors from the rug rather than all plain white and gray? Another throw in the red color as well as the creamy beige? What metal color are you aiming for? basic black? a deep copper/aged bronze that would coordinate with the grays and rug?
Wall art in the style /subject/colors you like. Do the frames in different sizes, but the frames identical style/color. Matting should flatter the art in the frame.
Sculpture of your choice- found objects from your travels, family keepsakes, whatever.

I don't see any lighting. Table and floor lamps can add warmth to the room.Pay ateention to your wall color and furniture tints when choosing bulbs.

Definitely round things, as others have suggested. You might also consider flowing draperies (nothing geometric, like box pleats), round-shaded lamps, vases filled with flowers, and accessories with organic shapes to them. Of course, you should also add some artwork into the mix. Check Etsy, Society6, etc for colorful art.

Incorporating any of those things would also be a good way to add color.

Seconding the idea for texture, though personally I'd skip a flokati as too hard to clean. Try some fabrics/rugs with sculptured but not hard-looking nap. Greenery, whether real or silk, is also a good way to soften a room. Personal objects will start taking away some of that hard, cold feel as well.

A big ol fuzzy Flokati rug!

To clean Flokati rugs: throw into dryer on air fluff for 10-20 mins. Do this monthly, and they stay in good shape.

A big French market style basket or two to store soft throws or magazines would help, since they are round.

Also, a tall ficus or palm in a big round planter would help add some softness and depth to the room.

Lots of texture! A knit throw blanket, some velvet pillows, and softer lighting would really help soften the look you have.

To me, the rug makes the space very formal. I would look for something a little more "fun".
Once you put the pillows on the chairs and couch, those lines will soften.
Some woven round baskets to put on the bottom shelves of the side tables (think rattan or sea-grass).
Maybe curtains with a pattern?
A colorful ottoman is a good idea.
Big plants always help.
And something whimsical (doesn't have to have ruffles) and something personal - either through artwork or accessories.

every room should have something living in it- a tree, if there is room, or if not, a simple trader's joe's orchid or flowering bromeliad. also, try to keep accessories light n bright- think whites and metallics. last, add in eclectic art and lighting that doesn't necessarily anythng else inteh room- things are looking pretty matchy-matchy, and matchy-matchy always makes a room seem flat.

oh yeah- the rug is a little grandma. try for something a bit hipper.

round things...coffee table, lamps, mirror, boston terrier, art, plants

I think the combination of the earth tones in the rug and the gray upholstery just does not work. I think that rug is wrong, wrong, wrong for the room based on everything else you have chosen. The rug looks old and frumpy, and the furniture looks cold and soulless - they do not play well together. (I'm sorry!!)

Add texture and curves -
A coffee table with curved lines in a warm wood tone
A few table lamps with interesting textures/shapes, maybe a burlap shade
A cozy woven throw
Plants

You have a good thing started. I'd see how it all shapes up once you get it in the room. It may not look as stark in a larger scale.

Change those drapes to something colorful and light, with a pattern that has curvy lines and you're nearly there.

I have a similar colored couch from room and board (http://www.roomandboard.com/rnb/product/detail.do?articleNumber=429760&an=0_429760), and have patterned curtains, as others have mentioned. That really changed the room, to give you more context (http://www.westelm.com/products/cotton-canvas-printed-window-panel-scribble-lattice-b901/?pkey=cpatterned-curtains). They completely changed the room and gave it the softness I was looking for. I also have a few pieces of furniture that are bold in color. They are in places so that they don't take over the room, but really blend with the other neutral pieces in the living room. And definitely add some light.

Why do you want to soften the look? I don't care for the rug. If this was my room, the only thing I'd add is fresh flowers and a couple of beautiful cats.

Definite yes on the flokati! I was looking through some old family pictures recently and saw ours - made the whole room warm and wonderful!

Oh, and don't be too quick to veto ruffles - I think West Elm had some plaid/ruffled (think tuxedo ruffle) bedding, which included pillows, recently...very warm, very classy, but still fun and soft.

I addition to round things, consider rounded square shapes. You can get them in all sorts of furniture.

I, too, would skip the rug and get something with pattern and texture - there are lots of attractive flat woven rugs around that will look fresher than the rug.

Don't buy so many black pieces. They are hard and cold.

Depending upon the color scheme you end up with, consider large African baskets on the walls, for color and texture. You can buy them online inexpensively. Group them. Also consider a pouf.

I like the things you have chosen, but everything looks linear and straight, and I think you need some curves and texures in there. I would go for a rug with an abstract desgin in bright colors, and I'd look for a pattern with swirls, circles, or curves. Something fun. I'm not into the flokati, but I have pets and maybe that's why. I'd pick a color or two from the rug and use it in pillows, throws, art, etc. Plants also soften a room, and I'd have more light sources.