Re-greasing need depends on the amount of miles and the type of abuse you give your bike. Most people probably don't need to regrease every year.

More frequently than regreasing, though, is to check your brake shoes condition and check all your fasteners (nuts, bolts, screws mostly) to make sure that they are not getting loose.

Also, check your spokes occassionally to make sure you have not broken any and to make sure they are all properly tensioned.

Check your tires to see that they are not wearing out, getting bald spots, or suffering from damage.