Filters, aka Tagged Questions, are still around.
It's just that the "Tagged Questions" nav link was replaced with a "My Filters" sub-nav link under "Hot Questions". So, to access your filters, click "Hot Questions", then click "My Filters".
EDIT: The "Tagged Questions" link was replaced with a "Filtered Questions" link, which only appears in the nav for logged-in users.
This was done to make the homepage more noob-friendly, since Tagged Questions are arguably a power-user feature.
"Shared filters" also haven't gone anywhere. You can still share the url to any filter, and the recipient will be able to view and save the filter.
We did, however, remove the "Popular Filters" page. It received little traffic and wasn't working the way we hoped it might. The most popular filters always seemed odd and semi-random. For example, these were the top 3 filters at the time the page was removed.
All Sites: [scm fortify] [git*] [hgignore] [hgrc] [hgsubversion] [mercurial] [msysgit] [rtc] [subvers*] [svn] [tortoise*] [version] [version-control] [versioning]
All Sites: [emacs]
All Sites: [ccrc*] [clearcase*] [cleartool] [rational-team-concert] [rtc]
These are hardly useful to the average user, let alone a new Stack Exchange user who happened upon the "Tagged Questions" link in the top-level nav.