This is a behaviour that should be intrinsic to WordPress but unfortunately it's not readily available.
The tagging structure is already at a mature level where a query to
will display all posts tagged apple and orange.
It would be very useful to be able to click on a series of tags and filter the results in this fashion while browsing.
For example, clicking on a tag for 'orange' on the home page will take us to
/tag/orange. Subsequently, clicking on 'apple' takes us to
/tag/apple. This is what we can call 'SURFING' the tags.
'FILTERING' the tags would be similar, but additive. Clicking on the tag for 'orange' on the home page will take us to
/tag/orange. Subsequently, clicking on 'apple' will take us to
/tag/orange+apple. Thereby filtering our results down to posts that are tagged with multiple tags.
Even better, it would be good if the widget on the sidebar would intelligently update itself to show only tags that are applicable in the new frame of reference.
The user should have a convenient way of switching between filter and surf mode.