In a medium pot, combine the rice, water and sugar. Cover with a lid and bring to a boil over medium-high heat and immediately reduce heat to lowest setting. Let the rice continue to cook for 15 minutes, then remove from heat.
Meanwhile, prepare all the vegetables and place them on a platter. Pour the vinegar over the cooked sushi rice and gently stir with a spatula.
Cover a bamboo sushi mat with plastic wrap. Place a sheet of nori on the mat. Scoop ½ cup of rice onto the nori and press the rice to spread it evenly up the edges. Add your filling of choice on the bottom third of the nori-rice sheet. Roll the sushi away from you with your hands, tucking in the vegetables as you go. Remove the mat from under the roll and place it on top. Press the roll into a compact rectangular log, and using a serrated knife, slice into ½-inch pieces. Serve with soy sauce.