Sarge81 said:
Do a visual inspection of the rubber part of the mount. If they mushed down to the point whereas there is metal to metal contact they should be replaced. Especially on the passenger side. The engine torques to the right whenever you push the throttle putting most of the pressure on that side.
With the hood open put it in gear and nudge the throttle and see if the driverside of the engine rises unusually high. Thats the side that likes to pull the rubber apart since the engine torques to the right. You most likely won't notice a ripped mount since the weight of the engine keeps them compressed.
I recommend not buying those cheap OEM style rubber isolated mounts. They fail fairly quickly I found though past experiences. Spend the money and buy some decent polyurethane mounts. You really won't notice any extra vibration with the poly ones.
Check your transmission mount while your at it too. Those can make some clunking noises under there if its bad.
Then put it in reverse and see if the other side rises....