Sounds like undersized joists.
Get a couple of 2x4s and put them under the center of the joists to the basement floor below to see if this helps. It will.
Then look into adding some joists along side the existing ones(sistering joists) or installing a beam.
A book at the library or a local contractor will be able to give you some more ideas.
Depending how many obstacles are in the way, pipes, wiring and duct-work will decide which course you take. Someone has already posted in the walls section something similar with pictures I believe.
This is common on older houses..the more weight we add to our homes the more they sink, creak sag and just age.