Traditional Area Rugs, Contemporary Spaces
I have a client who is struggling with this very issue. She has purchased a new contemporary sectional and in the same room has a very traditional area rug which one could argue does not "match" her new contemporary look.
Much like selecting art, I would argue that when purchasing a traditional area rug you should be selecting something you truly love. Many of my clients happen upon rugs while travelling, so having the luxury of coordinating the rug to the space they're looking to decorate is not always possible.
If you've selected a traditional rug in your travels regardless of how it looks with your contemporary furnishings, it should at minimum remind you of a time and a place, a trip you took, who you were with and how you felt when you made the purchase. In my opinion, that's it's true value. If it were to match exactly to the space you're decorating but you did not like it nor had a connection to it, then it wouldn't be of value.
Certainly you can strive to select from the area rug colours on which to base your furnishings but it can be difficult given the often pungent and instense nature of some of those same hues to avoid having a room full of primary colours. Make every effort to select one colour from the rug to work with, but don't feel it needs to be the strongest and most dominant one you see.
The truth of the matter is that much of the aesthetic of design is a matter of taste and is as such, subjective. When it comes to art and area rugs, love them and don't worry about being "matchy-matchy". If it happens to work in the space with all your furnishings, great. If not, at least you love it and it has meaning for you. Consider it a conversation piece.
Check out these images of some contemporary furnishings with traditional rugs. Again, the beauty of these rooms is a matter of taste.