OK, I like this thread for two reasons. First of all, like many others, probably every bike I own fits the OP's description! I have a "find bikes in the garbage" habit and a "buy cheap bikes on e-bay or craigslist if it's in my (relatively hard-to-find) size" habit. It reminds me of something I read on another forum once, "Would you rather have ten Yugos or one Porsche?" I am definitely a ten Yugos kind of guy, I admit.
Secondly, I like that the OP used one of my favorite Britishisms, "knackered," meaning tired or worn out.
According to Encarta's definition of "knacker":
1. somebody who kills horses: somebody who buys and slaughters old, worn-out, or injured horses for their body parts such as their flesh and hide
2. demolition merchant: somebody who buys and demolishes unwanted buildings and sells their materials for scrap
I feel that I am often doing this with bikes. "BikeKnacker" would be an awesome user name! So would TenYugos, now that I think of it. I should change mine....