Check your scraper bar to make sure it is even and without burrs. The scraper bar rubs against the ground and pulls the snow off the pavement. This bar will occasionally need to be replaced. If you let it get bent and misshapen, it will damage the housing of your snow thrower, and that will be a very costly mishap.
Feel the rubber paddles to make sure they are in working order. The rubber paddles are on the auger. If your finger slides between the rubber and the housing, its probably time to replace the rubber. At tighter fit that does not allow your finger to pass means the snow will be removed more efficiently.
Replace the spark plugs on a two-cycle engine. A two-cycle engine is quite easy to maintain, and changing the spark plugs is the biggest job. In addition to keeping it filled with an oil-gas mixture, you have to check the lube in the gear box. Grease this area liberally. If you have a four-cycle engine, you must add gas and check the oil. You will want to change it after every 20 hours of use, using 5W30 oil.
Take the belt cover off and check for cracks and signs of wear and tear. It is better to change your belts before a problem develops instead of afterward. Change the belts if necessary.