Make COUNT(*) Faster?

Hello all you PostgreSQL/SQL gurus!

I've started using PostgreSQL pretty recently, and I am quite
disturbed about the performance of a simple SELECT COUNT(*) FROM
table. What should (in my mind) be a nearly instantaneous operation
instead takes nearly 700ms in a table with only 87k rows of data!

If I run an EXPLAIN on this query I can see that it is doing a
sequential scan, which seems quite needless, as surely this
information is cached in some secret location.

It is very possible that I am missing something, so I ask you: is
there a faster way to find out how many rows are in a table? I've
tried doing a COUNT(column) where I have an index on column, but it
still does a sequential scan and it is still very very slow. What
are my options?

I offer you many thanks in advance,
Varun Mehta