I moved the stereo into a larger room in my home, and along the way, pulled up the carpet, installed a maple hardwood floor, and worried about the same kind of issue. The acoustics were hard, and the last thing I needed was bright, harsh sound. As I walked around, clapping my hands and yelling out, some major sweating over what would come sonically ensued.
Thankfully, the end result is very, very good. In fact, friends would listen to the same system, comment on the sound, and ask what upgrades I'd made at the same time. Only one, the room.
What I did had no planning in regards to the system, just the typical things one would put in a room. As things ended up, I needed no audio related room treatments. As has been mentioned, curtains were the first thing I did. While my curtains are fairly heavy, they aren't anything special. However, I also have a more sheer, gauzy type inside the curtains that show in the room. The combination of both likely takes care of the hard glass surface of the windows. Next, a nice, fairly thick (again, nothing out of the ordinary), wool rug. Mine is about 8' X 11', and I would advise one not to skimp on the size. In addition to providing seating, comfortable furniture did a lot more than I would have expected in helping out the acoustics. Some "unintended" room treatments, such as things to brighten up the room like plants, lamps with large shades, etc. played a role. Finally, flexibility in terms of loudspeaker positioning in the room will always make a major difference, and is likely the one parameter most people are hamstrung by. Thankfully, I had (mostly) total freedom there.
Again, what I feared being horrible, softened up nicely once the room was furnished. Once I hooked everything up, I was more than pleasantly surprised with how things came together.
