Add a UV Sphere to the scene and select an edge with AltRMB, next enter Face selection mode and select a face near the edge you marked. Next hit A to select the entire sphere and hit U > Follow Active Quads.

Note the grayed face near the middle of the sphere along the edge, this means that it had been selected before you selected the entire sphere and this is similar to what you should have done.

After unwrapping, you should get a huge UV map in the Image Editor. Transform it as desired, I would recommend aligning one corner of the map to a corner of the image and scaling it via the 2D Cursor.

A perfectly unwrapped sphere sans exponentially spaced UVs which aren't possible unless you tweak the map afterwards or modify the object's geometry.

You might notice a sharp seam near the top of your sphere where the texture stops. This is caused by the geometry of the sphere as the top vertices merge into a single point and the unwrap method basically ignores it.

To fix, just get an edge ring as close as you can to the middle vertex so that it won't be noticeable.

Update:

Newer versions of Blender now come with a Generate UVs checkbox (that can do as the name says and provides pretty decent maps) when adding a new mesh for most of the objects. Simply access this from the F6 menu or the toolshelf. This option is only available when generating a new object. The layout is below, still not perfect but useful nonetheless .

Add a UV Sphere to the scene and select an edge with AltRMB, next enter Face selection mode and select a face near the edge you marked. Next hit A to select the entire sphere and hit U > Follow Active Quads.

Note the grayed face near the middle of the sphere along the edge, this means that it had been selected before you selected the entire sphere and this is similar to what you should have done.

After unwrapping, you should get a huge UV map in the Image Editor. Transform it as desired, I would recommend aligning one corner of the map to a corner of the image and scaling it via the 2D Cursor.

A perfectly unwrapped sphere sans exponentially spaced UVs which aren't possible unless you tweak the map afterwards or modify the object's geometry.

You might notice a sharp seam near the top of your sphere where the texture stops. This is caused by the geometry of the sphere as the top vertices merge into a single point and the unwrap method basically ignores it.

To fix, just get an edge ring as close as you can to the middle vertex so that it won't be noticeable.

Add a UV Sphere to the scene and select an edge with AltRMB, next enter Face selection mode and select a face near the edge you marked. Next hit A to select the entire sphere and hit U > Follow Active Quads.

Note the grayed face near the middle of the sphere along the edge, this means that it had been selected before you selected the entire sphere and this is similar to what you should have done.

After unwrapping, you should get a huge UV map in the Image Editor. Transform it as desired, I would recommend aligning one corner of the map to a corner of the image and scaling it via the 2D Cursor.

A perfectly unwrapped sphere sans exponentially spaced UVs which aren't possible unless you tweak the map afterwards or modify the object's geometry.

Add a UV Sphere to the scene and select an edge with AltRMB, next enter Face selection mode and select a face near the edge you marked. Next hit A to select the entire sphere and hit U > Follow Active Quads.

Note the grayed face near the middle of the sphere along the edge, this means that it had been selected before you selected the entire sphere and this is similar to what you should have done.

After unwrapping, you should get a huge UV map in the Image Editor. Transform it as desired, I would recommend aligning one corner of the map to a corner of the image and scaling it via the 2D Cursor.

A perfectly unwrapped sphere sans exponentially spaced UVs which aren't possible unless you tweak the map afterwards or modify the object's geometry.

You might notice a sharp seam near the top of your sphere where the texture stops. This is caused by the geometry of the sphere as the top vertices merge into a single point and the unwrap method basically ignores it.

To fix, just get an edge ring as close as you can to the middle vertex so that it won't be noticeable.