Running Dry. Fire up the engine while it's on the trailer to make sure it'll start. You figure that in those few seconds the engine won't overheat. You're right, too. But the water pump's impeller can get damaged. Impellers need water for lubrication. Without it, they wear away or just fail completely.
Cheap Oil. Feed your two-stroke outboard bargain oil and ensure rapid aging. Don't think you're saving money when you buy some off-brand oil. To meet industry standards, oil has to pass the test only once, meaning it's not monitored by the batch. Better oils are uniform, consistently meeting the standard case after case. During the average summer, a 100-hp engine may burn only a gallon or two of oil. The difference between cheap oils and the ones offered by engine manufacturers may be about $10. Remember: The most expensive thing you can put in an engine is cheap oil.
First Coarse. Assume new filter elements are doing their job. Diesel engines, and gasoline engines running far offshore, should have two water separator/filters per engine. But don't put the same type of element in both filters, or worse, put the finer element in the first filter. Doing so makes that filter do all the work, with little to no benefit from the other. Put a coarse (30-micron) element in the first and a finer (2-micron) in the second. This way both share the load, do a better job, and give you longer element (and engine) life.
Shakedown. Engines will always vibrate, so you learn to ignore it. If your bowrail starts to shake each time the boat climbs on plane, but you don't feel it at the helm, it's likely that one or more of your prop's blades are bent. A vibration only at certain rpm could mean your prop needs balancing. When the whole boat rumbles and shakes at all speeds, the engine and shaft are out of alignment. If you want to see how and when your boat vibrates, watch the surface of a bucket of water placed in the cockpit.
Jets Suck. Water jets let you run in shallow water, so you go in freely. Unfortunately, you may not come back out. Jets use some of the water they suck in for cooling. If that water has sand, muck, or rocks mixed in, your cooling system may get clogged. One jet drive manufacturer goes so far as to warn: "Avoid shallow-water conditions." Continuing with, "Always be in at least two to three feet of water, especially when accelerating from idle speeds." If you must run in skinny water, go fast. This way the jet sucks in cleaner surface water as the boat rides high and well above the bottom.
Forget to Flush. Put your jet drive away after each use without thoroughly flushing the engine and you may have to put it away permanently. Although it may not ingest something large enough to cripple it while underway, it can develop a slow buildup of crud. Clean out internal passages by flushing your jet with freshwater for 10 minutes, and use plenty of pressure. All current models have a flushing port. Older Mercury jets can be updated with an accessory flushing attachment that costs about $25.