Shoot at the maximum resolution of the camera unless for some reason you're trying to save space on your memory card.
There are other valid reasons to lower the camera's resolution.
If you're not a serious photographer, i.e., your pictures are just happy-snaps for posting on the web, and you're sure you won't need to print them out at high resolution, then you can save a lot of hassle and time by just shooting at the target resolution.
Above and beyond the memory card space savings, shooting at a lower resolution means that you'll waste less time transferring files, waste less time waiting for image processing tools to work on the image (not just resizing, but things like color correction and sharpening too), and your overall storage space on the hard disk of your computer will be less over time.
There's another reason that you might want to shoot at a lower resolution. Some cameras allow the lower resolution to increase your zoom, without having to use "digital zoom" features. My camera does this and it calls the feature "EZ" zoom. It works like this:
Let's say your camera has a lens that will go to a 3X zoom. At full resolution, that's the most you'll get before you have to push into digital zoom (resampling). But if you're shooting at a lower resolution, it can, instead of resampling the image to the lower rez, simply use the pixels in a smaller rectangle in the center of the image sensor instead of the entire image sensor. You'll get a higher zoom level but still at a 1:1 pixel sample. In other words, the lens might be at 3X, but since only the middle 2/3 or so of the image sensor is being used, the photo ends up at something like 4x actual zoom.
It's the same as if you'd taken the high resolution version of the picture and cropped it down in photoshop after the fact. But you get the benefit of being able to zoom and aim at the higher zoom level on your camera's LCD display, and you don't have to do the post-processing.