The rule of thumb when dealing with load bearing structures is, whatever you take away you should replace in some way. While removing one stud should not cause catastrophic failure or anything it is generally not good practice. To determine if it is load bearing you can look in the roof space above the wall and see what direction the ceiling joists are running. If the ceiling joists run perpendicular to the wall below it is most likely load bearing. If there is not an roof space above there most likely will be another wall directly above the load bearing wall as was mentioned by an earlier answer.
In simple homes, looking at the construction design can be a clue. For example, in the graphic left, you can see that the wall shown is holding up an intersection of beams holding up the upper floor. This would be considered a load bearing wall.
When in doubt, assume the wall is load bearing and act accordingly!
It is easy to understand how renovations can cause weight to be transferred onto formerly non-load bearing partition walls. For example, the addition of exhaust fans and roof space stairways often requires cutting of ceiling joists, which can also transfer loads from the original walls... the main (center of the house) beam and the outside wall, onto non-load bearing walls that are in between them. Adding a room in an attic can change the entire load bearing status of the walls below.
To confuse matters further, some types of construction, such as post and beam or steel girder, may not have any bearing walls at all except for the outside walls. What's a mother to do??
Look at the structure of the house and ask the following questions:
- Is there a significant load above, such a built-up (multi-board) carrying beam or another wall? Is there a full floor above it, or just an empty roof space?
- If you can view the joists in the roof space, is the wall parallel or perpendicular to them? Generally, load bearing walls are perpendicular to the joists they support. If two separate floor joists or ceiling joists intersect over a wall, that wall should be considered load bearing.
- Is it an outside wall? You should consider all outside walls load bearing. If the house has been remodeled, a former outside wall could now be an inside wall. Examine the foundation to find these "stealth" outside walls.