Why should I care about lightweight vs. annotated tags?

I switched from Subversion to Git as my day-to-day VCS last year and am still trying to grasp the finer points of "Git-think".

The one which has been bothering me lately is "lightweight" vs. annotated vs. signed tags. It seems pretty universally accepted that annotated tags are superior to lightweight tags for all real uses, but the explanations I've found for why that's the case always seem to boil down to either "because best practices" or "because they're different". Unfortunately, those are very unsatisfying arguments without knowing why it's best practices or how those differences are relevant to my Git usage.

When I first switched to Git, lightweight tags seemed to be the best thing since sliced bread; I could just point at a commit and say "that was 1.0". I'm having trouble grasping how a tag could ever need to be more than that, but I certainly can't believe that the Git experts of the world prefer annotated tags arbitrarily! So what's all the hubbub about?

(Bonus points: Why would I ever need to sign a tag?)

EDIT

I've been successfully convinced that annotated tags are a Good Thing — knowing who tagged and when is important! As a follow-up, any advice on good tag annotations? Both git tag -am "tagging 1.0" 1.0 and trying to summarize the commit log since the previous tag feel like losing strategies.