There are various things you can check that might suggest that a given wall is or isn't load bearing, such as:

o If there is no wall or support posts in the basement beneath the wall in question, the the wall might not be load bearing

o If the joists of the floor above the wall in question run parallel to the wall, then the wall might not be load bearing

However neither of these checks is conclusive. There are really only two ways to know for sure:

o Take out the wall, and if something collapses, then it was load bearing.

or

o Consult a structural engineer, who can tell you not only whether the wall is load-bearing, but if it is, what would need to be done if you still want to remove the wall.

I am really big into DIY, and getting a structural engineer is one of the few things I paid someone to do in my extensive kitchen remodel.

You really have to get an engineer to look at it. We had a small (2 feet wide) wall that no one (several very experienced DIYers) thought was load bearing, based on its orientation, location, etc. But better safe than sorry, we got an engineer to come look at it and he concluded that it was actually carrying a significant load. Made sense once he explained it, but none of us would have recognized it without him pointing it out. The solution was simple (a new header in another location) and the peace of mind was priceless.

What is the style/age of your house? We bought a house 120 year old house a couple years ago and our contractor explained that old houses are often much easier to 'figure out' in terms of structural makeup (unless there have been half-assed renovations since it was built). What are the exterior walls made of? What is the layout? Have there been alterations to the original floor plan that you know of? Have you removed a part of the drywall or plaster on the ceiling of the rooms you are hoping to join? If you haven't, this would be your step in trying to figure it out. If the joists in the ceiling of the two rooms are running towards each other, chances are the wall is load bearing and you will find the joists are not continuous all the way across the house but actually end slightly past the wall you are looking to remove and the joist that continues across the other room begins a little before the wall and continues across the other room.