I have them all listed in a Word document, that's up to 230 lines. But some of those are in box sets and may include more overall discs/films while falling under one title in the document (the Godfather collection, for example).
So figure somewhere between 240-250.
It never occurred to me that there might be computer programs out there to catalog large collections.. duh.. hehe. I might have to check those out.
I need a bigger rack, too. The problem is price.. I'm one of those "poor" DVD collectors. The only reason my collection is so large is because I bought it piecemeal over the course of many years. Getting good deals on release day at Best Buy, things like that. $20 here, $40 there, rather than spending in big chunks (this is the same reason I don't yet own an HDTV).
My original rack, I bought for about thirty or forty dollars. It could hold maybe 150 DVDs. Wooden, with two side supports joined by 1x2s and dowels to hold the discs. Rather than buy a new one when it filled up (which would have cost me at least a hundred bucks, for a rack that could hold several hundred discs), I expanded it myself with a few dollars worth of wood from Home Depot, to twice it's original width. But now it's filling up again (no thanks to Stargate and Star Trek, each of which takes up almost a full shelf). I'm debating on whether I want to move those somewhere else, or expand the shelf again (which will require a third support in the middle, since it looks oddly bowed in the center from the weight.. DVDs are surprisingly heavy in large numbers).