Optional: Reduced-sodium soy sauce, prepared wasabi and pickled ginger slices
In a large saucepan, combine rice and water; let stand for 30 minutes. Bring to a boil. Reduce heat to low; cover and simmer for 15-20 minutes or until water is absorbed and rice is tender. Remove from the heat. Let stand, covered, for 10 minutes.
Meanwhile, in small bowl, combine the vinegar, sugar and salt, stirring until sugar is dissolved.
Transfer rice to a large shallow bowl; drizzle with vinegar mixture. With a wooden paddle or spoon, stir rice with a slicing motion to cool slightly. Cover with a damp cloth to keep moist. (Rice mixture may be made up to 2 hours ahead and stored at room temperature, covered with a damp towel. Do not refrigerate.)
Sprinkle toasted and black sesame seeds onto a plate; set aside. Place sushi mat on a work surface so mat rolls away from you; line with plastic wrap. Place 3/4 cup rice on plastic. With moistened fingers, press rice into an 8-in. square. Top with 1 nori sheet.
Arrange a small amount of cucumber, crab and avocado about 1-1/2 in. from bottom edge of nori sheet. Roll up rice mixture over filling, using the bamboo mat to lift and compress the mixture while rolling; remove plastic wrap as you roll.
Remove mat; roll sushi rolls in sesame seeds. Cover with plastic wrap. Repeat with remaining ingredients to make 8 rolls. Cut each into 8 pieces. Serve with soy sauce, wasabi and ginger slices if desired.