I was just noting on another thread that cilantro tends to reseed itself and spread quickly, but it's easy to uproot so not a big problem. More annoying are the plants that spread via underground roots, like mint - I have to do some major root-ripping each spring to prevent my herb patch from become a mint meadow.
But the worst by far that I've encountered is horseradish. I planted some about ten years ago in a community garden. Nothing much happened, so I assumed it didn't "take" and forgot about it. The following year, suddenly there was this huge plant that looked like a small palm - sure enough, my horseradish had established itself. But at the end of the season the root was no better than those I get at the supermarket, so I pulled it out and figured I was done with it. No such luck.
The following year there were bunches of horseradish plants growing all around the area of the first. That's when I did some research and discovered that it spreads via deep underground roots, and that these roots are very fragile, and that any part of a root can establish a new plant. In the end I had to completely dig up an area of several square yards, to depth of close to 18 inches, and literally sift all the dirt to get rid of every bit of root. Shortly afterward I moved to where I am now, and have my own garden, so I hope it didn't come back to plague whoever inherited my community plot.
Anybody else got a good plant invasion story?