Andy Pols and I presented this paper at XP-2004 in Garmisch-Partenkirchen. It describes an approach to legacy systems that is non-intrusive and relatively low-risk.
Martin Fowler named this approach Strangler Application
Abstract. We describe how a small, successful, self-selected XP team approached a seemingly intractable problem with panache, flair and immodesty. We rewrote a legacy application by delivering new features, a radically different approach to those previously applied. This proved to be a low cost, low risk proposition with a very high payoff for success. Most importantly it provided users with new functionality quickly that could never have been retrofitted into the legacy system. In the longer term it may give a migration strategy for replacing the legacy system.
Download the full paper here: An agile approach to a legacy system [84K PDF]