I really don't ship anymore, mainly because - and I'm sure Drtooth can back me on this - fandoms have ruined the fun of shipping for everybody. Case in point: the Chipmunks fandom; there's a serious divide between canon shippers and mixed shippers, and each side is so die-hard into their shippings, that they'll practically go to war with anyone who disagrees with them, and I've seen more than my fair share of these kinds of flame wars over at deviantART - it gets really ridiculous at times.
That said, it's no secret to anyone who's followed me on dA all these years that I used to be a really big Simon and Jeanette shipper: I even coined the ship name "Simanette" and used to do a whole lot of Simanette fan art too... but again, it was the craziness of the fandom and the divide between shippers that really turned me off of shipping, as far as being a Simanette shipper, I do believe that ship has sailed.
Admittedly, I have shipped other couples before. From HEY ARNOLD! I was on the Harold and Rhonda ship for a very short period a few years ago; from SST, when I was younger I would ship Cookie and Prairie, simply because they seemed to make a cute (not "cute" in an adorable way, but more like in an amusing, funny way) couple. Right now, I'm trying really hard to resist an ARTHUR femslash ship: Prunella and Marina.