You need to be careful when dealing with load-bearing walls... OK, so much for forewarning...
If you can see any ceiling rafters, they will be running perpendicular to the load-bearing walls... (wall running parallel are just partition walls.)
If you can't see the rafters, go to the floor above - if you have any floor-mounted heating grates, pull one up - you may be able to see the floor joists. (If you have a rectangular grate, generally it will sit longways across two joists.) Again, the joists are perpendicular to the load-bearing walls. (So any wall running the same direction as a long,rectangular register grate will be load-bearing.)
Another way to tell (This method is a bit dubious) - a load-bearing wall will usially run down the center of the house - or else you will have two load-bearing walls that divide the house into thirds. These walls run the entire length of the house, except for where the doors are. Whichever way these walls run, you can expect that the load-bearing walls on floors above and below will run the same direction. If the walls only run across half of the house, they are probably partition walls.
Also, the staircase will generally (but not always) run parallel to the load-bearing walls -> this is again, very dubious.... If the hallways by the stairs are parallel to the stairs, then the walls may be load-bearing. If the halls are perpendicular (i.e. the stais go up and connect to a hallway, making a "T") the stairs are probably not parallel to the load-bearing walls.
Another clue - load-bearing walls usually sit on top of each other from floor to floor. So if you have walls in the same position upstairs as downstairs, those are probably the load-bearers.
These suggestions are meant only to be clues - not absolute fact. It depends on how complex the floorplan of the house is. And load-bearing walls can sometimes be perpendicular to each other (although in simple floorplans, they are generally parallel.) Take all of these things into account together, and still proceed with caution. (call an expert.)