All small-engine manufacturers suggest changing the engine oil in your mower at least once per year, and more often for commercially used mowers. The owner's manual for your mower should have a recommendation for what oil to use under varying conditions.
Single Viscosity SAE 30
Operating at temperatures above 32 degrees Fahrenheit, TecumsehPower and Briggs & Stratton recommend Single Viscosity SAE 30 motor oil. Honda and Kohler suggest SAE 30 motor oil for summer-time operating temperatures, but not below 50 degrees.
Honda and Kohler recommend 10W-30 as the standard oil for their engines, under most operating conditions. TecumsehPower and Briggs & Stratton suggest 10W-30 only at low operating temperatures (below 40 degrees Fahrenheit), which you would rarely encounter when mowing. Briggs & Stratton indicates that multi-viscosity oil can increase oil consumption in its engines.
Briggs & Stratton suggests that synthetic 5W-30 provides excellent all-weather protection for its engines, with improved ease of starting and low oil consumption. Other small-engine manufacturers suggest synthetic 5W-30 only for extremely cold operation--more likely when using your snow blower rather than your lawn mower.