Landscape- This works for landscapes mostly because of the amount of image it fits into the frame. This in addition to the lighting settings it changes makes it great for landscapes.
Effects- I almost never use this setting on the camera. However, in theory, there are some neat effects. I say these in theory because they are only cool if they work. This effect was a color filter. As you can see, it worked to some degree.
No Flash- Whenever I take pictures, I never use my flash. I never use this setting because I can turn the flash off while still using other settings (or by holding it down). However, it is nice if you want a picture to look more natural and compensate for the lack of light by having the shutter open longer.
Portrait- I am not a fan of this setting, and I don't see much benefit from it. I tend to like the looks better on different settings. Really, I see nothing that it does that I happen to like just for portraits.
Sports- This is a great feature to have. It lets you hold down the button and it takes pictures in rapid-fire. This combined with the fast shutter speed makes for less blur and a crisper image when someone is moving.
Indoor- This one is pretty straight-forward. It changes the settings to allow more light to compensate for the lack of light when indoors. I use this setting only occasionally because I use other settings that I still prefer indoors over the setting meant for indoors.