I notice on Librarything you can create new collections; make one for short stories, maybe? Or just open a text file and add each one as you go, with the link to it if it's online?
Mostly I don't keep track of my reading anymore; I used to, but now if I come across a story I've read before either I recognise it or I don't; if I don't and it doesn't strike me as bad right off, it's probably worth reading again.
There are a number of e-zines out there, and if you like SF there's the likes of
http://freesfbest.blogspot.com/, which will point you towards many of the sites out there with SFnal short fiction. Lots of good stuff on that one.