For an interesting variation on the Gaussian Blur effect, try Compound Blur (in the Blur and Sharpen category). You apply compound blur to the layer you want to make blurry (or partially blurry), but you need another layer in your timeline as well.
This extra layer should be a grayscale layer. It can be a gradient that you make in Photoshop. You can also make grayscale layers in After Effects, but if you do so, you have to Pre-compose them before using them for the Compound Blur effect.
Regardless of where you make your gradient layer, Compound blur will overlay it on top of the layer you're blurring. (It doesn't literally need to be on top in the Timeline). It will use this overlaid layer as a filter for the blur effect. Wherever the overlay layer is white, the blur will have full effect; wherever it is gray, the blur will have partial effect, and wherever it is black, the blur will have full effect.
Try this cool recipe:
Add a movie or still image layer to the comp.
Duplicate the layer.
Apply the Stylize>Find Edges effect to the dup.
Pre-compose the dup, selecting the "Move all attributes" option.
Turn the pre-comp's eyeball off.
Apply Blur and Sharpen>Compound Blur to the original layer.
In the Effect Controls palette, choose the pre-comp for the Blur Layer property.
For variation, open the pre-comp and invert the Find Edges effect. Or, replace the Find Edges effect with the Adjust>Threshold effect.