Indeterminate vining tomatoes, in fact, need a little more care than the determinate varieties. You have to pinch off the little side shoots (also called "suckers") that grow in the V between leaf stems and the main vine, and sometimes also at the base of the vine. This practice will ensure that the main vine grows strong and produces as many tomatoes as possible.
Sometimes you'll miss a side shoot, and you'll notice it only when it's already grown into a bigger branch. I still go ahead an pinch it off, unless it's grown blossoms in the meantime.
Pinching off side shoots is an easy task, though it can take a surprising long time when you have lots of plants. Besides making the main vine stronger, it will also give you the opportunity to inspect your plants, and check them for signs of disease or pests.