The structure of a home depends upon a network of components all working together to form a safe and strong building envelope. Most homes in the past half century or so have been designed by builders with the help of architects and building engineers and more recently with building inspectors being the last person to approve the actual building construction. Even with all these people involved in the building process it does nothing to stop the home handyman from cutting out walls or taking out critical posts to make the home more suitable to the inhabitants. Of course the problem with changing walls and tele-posts is that the entire structure may be counting on them for support.
Often people can get away with these renovations because the engineered plans have some room for error and the removal of a support wall will simply place the load on the trusses and outside walls. What often develops over time is the outside walls begin to spread outward as the roof settles inward. The drywall over the windows, doors and ceilings begins to crack, door jambs shift making the doors out of square and sticky. Other times the movement is far more serious and the homeowner will use a cable in the attic to hold the walls together, yes I have seen this more then a few times. So the long and the short of it is that you should seek the advice of a structural engineer if you plan to remove a wall or supporting post in the basement. Failure to do so could compromise your entire home. Almost anything can be done if you plan for the change and improvise a safe and effective solution.