Clipping is great, except when you don't want to alter the original geometries, such as when you want to select overlapping features. Or, in other cases, you just want filter the geometries based on nonspatial attributes. To achieve both of these results, you can utilize the Selection tools in combination with Save Layer As.. to extract just the features of interest. This recipe uses spatial selection methods to extract a subset of original polygons without altering them.
geology.shp that overlap with Wake County (census_wake2000.shp) by navigating to Vector | Research Tools | Select by location.census_wake2000.

When in the Save As... (as described in Chapter 1, Data Input and Output) dialog make sure to check the box next to Save only selected features.
This really goes back to the same fundamental concept of Intersection that most vector analysis rely on. When you can test whether two features overlap, there are many different operations possible based on the answer. You can select, deselect, or, as in the previous recipe, select then cut to fit. In these cases, each polygon is tested for at least a partial intersection, and the matches are then highlighted as the results.
While this recipe demonstrates how to select a subset of data based on location, you can also do the same thing based on attributes of the features with a query on the attribute table. Or, you can combine attribute based selection, spatial selection, and hand selection graphically on the map—any selection combination that you want can be saved as a new layer.
You may also notice in the Select by location tool that vectors can also be added or removed from existing selections in case you want to perform more complicated operations involving more than one type of criteria.