It is much more convenient and cleaner to use a single statement like
import java.awt.*;
than to import a bunch of individual classes
It clutters your namespace, requiring you to fully specify any classnames that are ambiguous. The most common occurence of this is with:
import java.util.*;
import java.awt.*;
...
List blah; // Ambiguous, needs to be qualified.
It also helps make your dependencies concrete, as all of your dependencies are listed at the top of the file.