I first realized my motor mounts were gone when my fan shroud and fan connected / self destructed.
From
http://www.babcox.com/editorial/us/us50126.htm ...
Most mounts are designed so that separation won?t allow the engine to fall out onto the roadway. But a bad mount may cause a myriad of problems - many easily misdiagnosed.
Often, bad motor mounts allow the engine to rock and move around, causing noise and interference problems with the throttle, transmission and clutch linkages. For example, a thumping noise when the transmission is put into gear or when the vehicle is accelerating is a classic symptom of a bad mount.
Excessive engine rocking also can create exhaust leaks and rattles where the head pipe joins the exhaust manifold. Plus, the donut that seals the exhaust joint can be crushed or broken by the motions of the engine, or the head pipe or pipe flange may crack.
Cracked or broken motor mounts can be an annoying source of vibration and noise, typically a clunk or shudder when accelerating hard. A broken or separated mount may even allow an engine-driven fan to scrape the fan shroud or contact the radiator, which also contributes to annoying noise.