Your for loop looks good.
A possible while loop to accomplish the same thing:
int sum = 0;
int i = 1;
while (i <= 100) {
sum += i;
i++;
}
System.out.println("The sum is " + sum);
A possible do while loop to accomplish the same thing:
int sum = 0;
int i = 1;
do {
sum += i;
i++;
} while (i <= 100);
System.out.println("The sum is " + sum);
The difference between the while and the do while is that, with the do while, at least one iteration is sure to occur.