Don't you love it when that happens? Actually, the street I grew up on never gets plowed by the city, there's just too many streets here, but my dad used to plow and his friends would come and do it for us if they had time. But yeah, it always happens that you spend hours shoveling yourself out and chopping the ice (a chore we had to do with this giant, insanely heavy ice breaker made of iron), and then the plow comes by.
Around here, you want something plowed you just have to shovel it yourself. At my college house I had to shovel a double-wide driveway, plus the sidewalks and paths (required by law), and also the street in front b/c our friends would park there. It took hours but it was great exercise.