Don't just let them go on their own. Tomato plants must be pruned to promote a healthy growth. Once the first flowering occurs, prune all leaf stems below the flowers. Stake now, carefully and gently to avoid damaging stem. Here is a great article detailing the job. http://www.finegardening.com/how-to/articles/pruning-tomatoes.aspx
I might go even further and remove more leaves. Another author indicated he ran his farm off of 3 leaves per plant after fruiting/flowering. It must be the top of the stem where the vine is still growing.
***Tomatoes can really grow on their own. They just need some great soil, water and a whole lotta sunshine.