Lot of things, I'll assume that it is not making any weird noises or you wouldn't have tried it out. This eliminates any major mechanical problems, for now.
Pull your plugs, are they cruddy? If they are, replace them since you just bought it. While your at it check the wires, is the insulation cracked? You can check this by making a tight loop in the wire and looking at the insulation on the outside, if its cracked replace them. Another check is to crank it up in the driveway in the dark, if it looks like a mini thunderstorm, same deal. If the wires check out, clean all of the connections of any corrosion when you put everything back together.
If all of that checks out try backing out on your fuel mixture settings and see if it improves. Does it ? It may be as simple as a mixture adjustment but can mean that you have a cruddy carb and need to clean out both of them.
How long has it been since the fuel pump was serviced? Just before the diaphram craps out you can have fuel delivery problems, it is rare but it does happen.
Back to the ignition, do you have spark on all cyls.? Check this by disconnecting all of the plug wires and one at a time insert a screwdriver into the terminal and have a helper crank the motor over. You should get a spark at each plug. If not you have a bad coil / powerpack. Be careful when you do this, it will shock you if you make contact with any of the metal.
If this still doesn't reveal anything, the timing/syncrhonization may be out af adjustment or you may have bigger problems. Does the powerhead get really hot after being out on the water for a short while. It shouldn't. This could be a stuck thermostat, faulty water pump, or big mechanical problems.(bad rings)
If you have any more questions pm me, I'll be happy to help you more.