Prev/Next in category (with the tag repeating for multiple categories)

Prev/Next day

Prev/Next week

Prev/Next month

Earlier/Later (like prev/next day, will not just go earlier in a particular context, e.g. not just earlier posts in january, but when the earliest january post is found, it'll go to september.

Built in 'breadcrumbs' i.e. 'where am I' - ideally will show all possible contexts, e.g. on an individual post it will show Home >> Cat 1 >> Cat 2 (for each relevant cat)
as well as Home >> Year >> Month >> Day
This'd be configurable, so a user could have primary category only, all categories, date breadcrumb only etc.

The category list should have options to show only parent categories and subcategories (to a user definable depth). It should be possible to easily show all first level categories, with relevant subcategories expanded (optionally with n children categories expanded).

E.g. a post in Cat B > Cat 3 might have

Cat A
Cat B
Cat 1 ('uncle' cats would have appropriate class for hiding if needed)
Cat 2
Cat 3
Cat i
Cat ii
Cat 4
Cat C
Cat D