In the "How Stuff Works" bittorrent article
http://computer.howstuffworks.com/bittorrent2.htm I read
   "if you run BitTorrent client software after your download
    your future download rates improve because you are ranked
    higher in the 'tit-for-tat' system."

Where is that tit-for-tat ranking stored for each of us?
How would I find my own bit torrent credit/leech score?
If I reinstall the bittorrent client, do I have to start all over again?

The tit-for-tat in BitTorrent only applies to the CURRENT download.  Each
peer looks at how much data you have uploaded to it during the current
session, and uses that to determine whether or not to send you data.[1]  
The more data you've sent it, the more likely it is to send you data.  
However, the peers have no memory.  Your uploading behavior on Torrent A
has no impact on your downloading behavior on Torrent B, because (1)
you're highly unlikely to be connected to the same peers, and (2) even if
you are, they don't use Torrent A's behavior in determining Torrent B.

So leaving the torrent running after the download is complete (i.e.,
seeding) doesn't affect future downloads.  It doesn't even effect the
current download, as you're no longer downloading data after the torrent
moves into seeding mode.  

What seeding does accomplish is even distribution of the file, with as
few people as possible stranded.  Over the lifetime of the swarm, the
total data uploaded must equal the total data downloaded (plus the size
of the original seeded file, which of course was never downloaded).  If
you quit the torrent having only uploaded 75% of the file, one of two
outcomes *must* occur: someone else uploads 125% (or several people
upload a total of 125%), or someone is stranded with 75% of the file, and
no seeds.  So those who don't seed are jerks: either they tease those
they strand, like dangling a piece of candy just out of reach of the
child, or they force others to do their work for them.

The only occasion where seeding on one torrent may iumpact another
torrent is on trackers that enforce a certain share ratio.  As someone
else has mentioned, this is calculated by the tracker based on the stats
your client submits at the start and stop of each session.  Your share
ratio is simply (amount uploaded)/(amount downloaded).  If the trackers
enforces a ratio, and yours falls below it for a certain period of time,
the tracker will just ban you for downloads.

For example, say your ratio on Tracker 1 is below 0.5.  You launch a
torrent, trying to download a new file.  You send a message to the
tracker of the sort, "Please send me a list of IPs participating in swarm
A.  I'd like to download."  The tracker responds, "No way; you'll just
abuse the system." End of story.  You're banned.  You could, of course,
go to a different torrent on Tracker 2, and operate just fine.  But say
you really want Torrent A.

To get A, you go back and dig up Torrent B, which you downloaded a week
ago and bailed on as soon as you hit 100%.  Launch Torrent B again, and
this time your client says, "Please send me a list of IPs participating
in swarm B.  I'd like to seed."  Since there's no way you can take
without giving back (since there's nothing left to take), the tracker
responds, "Certainly!"

You then seed Torrent B until you have an acceptable share ratio.  The
ratio can only go up, because you're uploading data, but not downloading
any.  Once the ratio is good, you can launch Torrent A again, and having
redeemed yourself, the tracker lets you in this time.  (The exception to
this scenario is some private trackers where a ban results in the total
purging of your user account, after which you can't even seed.  But
that's usually only for habitual offenders.)

Even with the tracker enforcing this level of sharing, once you join
swarm A and start downloading, your download speeds are only influenced
by your uploading speeds for swarm A.  All the speed negotiation is done
one-to-one, between your client and another client.  Neither the tracker,
nor third parties in the swarm have any idea how fast data is moving
between any two peers.

[1] In fact, some abusive clients exploit this.  They'll connect and
disconnect rapidly, creating new session after new session, and trick
peers into sending more data than they otherwise would.  Such clients
tend to get banned at the tracker level fairly quickly.