While there's no doubt that catalytic converters have done a tremendous amount of good in terms of keeping our air and groundwater clean, they can cause some serious performance problems. Even when new, converters cost a bit of performance and fuel economy; failure can easily exacerbate those issues.
Converters and Fuel Economy
A little bit of exhaust gas in your engine's cylinders can actually increase fuel economy when it's properly metered; that's the principle on which exhaust gas recirculation -- EGR -- systems function. However, those gases enter the cylinders through the intake through the intake valves, are metered by the EGR valve and compensated for by the fuel injection system. Blocking the exhaust traps excess exhaust gases in the cylinders, which disrupts the combustion event and causes the engine to run less efficiently.
It should be noted, though, that the "clogging" that most people think of isn't "clogging" in the sense that it's foreign material lodged in the converter. The converter's "washcoat" does get "clogged" with microscopic contaminants like sulfur, but those just render the converter useless by "poisoning" it. Most often, a "clogged" converter is a converter that has overheated and failed internally, causing the core matrix to collapse in on itself and block the passages that allow exhaust gases through. for this reason, a converter that's "clogged" enough to block exhaust flow must be replaced.