Yes, petrol/gasoline sitting in a tank will absolutely expire. Gasoline is not a single compound, it is a blend of hydrocarbons, some of which are heavier (longer chains) and some of which are lighter (shorter chains). Over time the light fractions evaporate, leaving the heavier ones behind. Reactions with oxygen can also slowly polymerize the hydrocarbons, further thickening the fuel and impacting its ability to vapourize and burn. This heavier fuel can burn less cleanly, leaving gummy varnish-like deposits in the engine, gumming up filters, etc.
Fuels also change depending on the time of year and the location. In places with cold weather the fuel at the pumps in winter is produced with more light fractions to assist with evaporation and ignition in colder weather. This "winter fuel" loses its light fractions much faster once warm weather comes and tends to be the type of fuel that expires most quickly. In hotter climates and in summer the fuel tends to be heavier out of the pump and expires less quickly, but in all cases old gas is a recipe for fouling up filters, injectors, and the engine itself.
Premium fuel is less likely to contain ethanol, but many still do. As noted in other answers, this also can take up water or evaporate itself, giving another mechanism that ages and fouls the fuel over long periods of time.
Just toss it and fill with fresh fuel. I always empty the tanks of any seasonal equipment that is going into storage until the next year and refill with fresh. Any fuel that doesn't get used that season just gets siphoned out and put into the cars (which will happily use it up). The engines are then run after removing the fuel until they stall from complete fuel exhaustion to make sure no old fuel is left in the lines, filters, etc. Best to not store your equipment with any fuel in it at all.