Changing the spark plugs is not a bad idea. They are consumable items, designed to be replaced as they wear out, cheap, and easy to do. Why not? BUT if that does not work ...
A common culprit is bad fuel. Two possibilities: water in the fuel, or old fuel that has degraded to a point where it combusts poorly. You wouldn't believe how many truly mysterious symptoms stem from bad fuel. Generally poor quality fuel and the addition of ethanol (attracts water, degrades non-metal parts) make this more and more common. The octane rating (burn-ability) of the fuel goes down as it gets old and eventually it just becomes unusable as fuel.
(There is a third possibility related to fuel, but that involves debris that clogs up the tiny passages in the carburetor. That's a whole different problem that only gets fixed by a) changing out the fuel and the filter and THEN b) cleaning the debris out of the carburetor AKA disassembly/rebuild. Not going into that here!)
I would dump the fuel tank and refill with fresh and see if that solves it. If the carburetor has a little brass drain plug in the bottom of the fuel bowl, take that out, drain the liquid (see what comes out if you can catch it) and refit it. If no plug, just get it running long enough to use up the old fuel and get new fuel through the system.
See if that alone doesn't fix it.
If you have an inquiring mind, when you dump the old gas, pour it into a clear container and see if it separates into water on the bottom and fuel on the top. If it does, you'll be saying, a-HA!
You changed out the fuel and the problem is not solved? If no joy, further and more systematic troubleshooting will be required. I would start by making sure the fuel supply system is not leaking air anywhere between the carburetor and the fuel tank and every hose in-between. I have seen bad primer bulbs (it won't pump up tight like it usually does), loose hose clamps, and bad pickup pipes in the (brand new) gas tank.
The problem is generally either electrical-related or fuel-related. Fuel system problems are easier to troubleshoot first. Determine if the problem is too MUCH fuel or too LITTLE fuel. Here's how:
While running at full throttle (not on the bench, but in the boat and underway), unplug the fuel line. It will run for a minute or so on the fuel in the carb bowl, then run out of gas. BUT: In that 2 seconds before it runs out of gas and quits, if it suddenly runs better as the carb goes dry and the mixture leans out, that is an indicator that the problem is too MUCH fuel. I'd look at the carburetor. Plug in the fuel line, pump up the bulb, restart, and head for home.
But if that trick doesn't make a difference, and while running for home at full throttle again, point a stream of propane gas from an unlit propane torch into the carburetor throat. You are supplying extra fuel for just a moment to the system. If the engine suddenly clears up and runs strong, thats an indicator that the problem is too LITTLE fuel. Go home and investigate that!
If neither of these tricks makes any difference, then you can probably eliminate the fuel system and begin looking at electrical problems. As one poster suggested, changing spark plugs is cheap and easy and sometimes plugs just go bad, so if you didn't do that first, try it now and you may find your solution right there.
After that it gets more complicated. Run the engine in the dark with the cover off and look at the spark plugs, plug wires, and coils. The darker it is the better. Look for anything glowing or sparking ... sometimes old plug wires will allow the "fire"to leak out to ground before it gets to the spark plug, and if that's so, you'll see it.
After this, you'll either need to find more troubleshooting tips or take it to a mechanic. I once had a most baffling problem with a my Yamaha 30hp and got a great tip (the one above about diagnosing too much or too little fuel) from the website http://www.maxrules.com. Click the tab "Technical Assistance" and then "Troubleshooting Tips"and you will find a very systematic diagnostic rundown. If you're still stuck, you can have a paid phone consultation with Bill Kelly, the "MasterTech." I have done this myself and he helped me solve the mystery. Good guy, money well spent.