Is there a way to style differently the "active" (just clicked) link on WP's "Categories" / "Recent Posts" / "Recent Comments" / "Blogroll" and other rather standard widgets displaying collections of links?

Consider http://wordpress.org/showcase/tag/people/ as a prototype of the desired effect: under the "Popular Tags" in the left column, the link "People" has presently been clicked. Note that "People" is gray and is not clickable. It looks like this:

Popular Tags
CMS (83)
People
Technology (60)

Then, click the blue "Technology (60)" link: it leads to http://wordpress.org/showcase/tag/technology/. Now, "Technology" becomes gray non-clickable, and the link "People (64)" became clickable again:

Popular Tags
CMS (83)
People (64)
Technology

I found an answer for "Categories" widget but not for the other kinds of widgets. CSS insert

PHP Code:

li.current-cat a {
    color:#FF66FF !important;
    border-left:7px solid #FFDDDD !important;
}
li.current-cat
{
    color:#66FFFF;
    background:#EEEEEE none repeat scroll 0 0;
} 


or

PHP Code:

li.current-cat, 
li.current-cat a {
    color:#FF66FF !important;
    border-left:7px solid #FFDDDD !important;
    background:#EEEEEE none repeat scroll 0 0;
} 


... works for "Categories" widget because the currently chosen list item will have an added class="current-cat" under the "li" element (I guess it's WP's feature, not the themes?).

However the "Recent Posts" / "Recent Comments" / "Blogroll" widgets don't seem to provide any means to tell the currently selected item from the other items on the list (again, I guess it's WP's feature, not the theme's)... Any thoughts?

it falls in the lap of the widget author. If they don't output something unique then there is no way to style it.