Ok confusing metaphor aside - the direction of light makes a HUGE difference on the quality of your picture.
Ideally the light will always be behind you and not behind the subject of your photo.
Light In Front
See how the clarity and colors are SO much better when the light is in front of your subject?
It's not always the natural state of things though... In my apartment the best angle to see my living room doesn't work with the light - drats.
This is a picture I took of my place a few weeks ago on auto. All of the light is from behind the living room, so it's creating a lot of shadow - just like the pot above.
We'll there are a few things you can do.
1. Mess with your photo settings to help with the brightness. I messed with shutter speed and ISO (slower shutter speed and higher ISO) and it made a big difference.
2. Choose a time of day when the light is less bright outside. It's about balance - not so bright that it overwhelms your room, but not so dim that you can't see your room. Experiment! You can check out a slideshow of my experimentation from Day 10.
3. Reflect the light within the room to balance out the shadows the light causes. A white sheet will make a big difference, or better yet a reflective Emergency Blanket. Just hang it up behind you and let it bounce the light around. (I got this idea from Photojojo.)
4. Mess with angles and see what happens with the light. It makes a difference even when the light is angled just a little more.
None of the pictures above were edited, so you really can do this with a little leg work! If you edit them, they look even better :)
Short of renovation that includes moving or enlarging your windows, working with what you've got is what it's all about with indoor light. Try a few angles and see what you come up with :)