If the database schema allows so, you can add geometry-less features in QGIS if the layer can be added as a non-geometric layer: SpatiaLite and PostGIS support this functionality if you enable the "show tables without geometry" option in their respective dialogs. Among the "tables without geometry" there will be also a "duplicate" (so to say) of the tables with a geometry field.
You can add both items for a single table and get two layers for one table.
The non-spatial layer will allow you to add new features (via the
+ button in the attributes table) where the
geom field can be NULL (I repeat, if the database schema allows so):
Shapefiles don't allow this kind of work-flow as far as I know. It may not be orthodox, but it works and it can be useful in certain cases.