My bet would be:

1) Web embedding products (directly exporting results for web code).

2) Big-data collecting and analysis.

3)  Automatic online data retrieving (it exists but is still not that common).

4) Real-time data collecting and processing for smart grids of GIS information (Any modern electric grid or urban traffic control does this but I believe you still need very specialized software).

And I would also add:

a) High quality rendering of image and animation for presentation.

One last point that does not depend only upon GIS developers and users (although they're included) is getting a true scientific standard for data (for files and memory structures). There are a lot of quality data standards that are horizontal towards scientific and industry areas but they're just no widespread enough.

My bet would be:

1) Web embedding products (directly exporting results for web code).

2) Big-data collecting and analysis.

3)  Automatic online data retrieving (it exists but is still not that common).

4) Real-time data collecting and processing for smart grids of GIS information (Any modern electric grid or urban traffic control does this but I believe you still need very specialized software).

And I would also add:

a) High quality rendering of image and animation for presentation.

One last point that does not depend only upon GIS developers and users (although they're included) is getting a true scientific standard for data (for files and memory structures). There are a lot of quality data standards that are horizontal towards scientific and industry areas but they're just no widespread enough.

Some additions to above

Web Ontology / Semantics for GIS and its implementation for real time use is an important area where developers are facing challenges. This will make GIS usage on Web more intuitive for many application areas. 

I agree the former answers and I also would add the integration of real 3D and 4D data, because in some sense GIS are still working with 2.5D datasets.