There have been vaginal births of triplets and even homebirths as mentioned by other pps, but they are not common, and for good reason. I was where you are, except that I only had one other child. My biggest advice is be open to things not going as planned. Shoot for a vaginal birth and do everything you can to help yourself get there, but don't beat yourself up if it doesn't happen. And, make sure your doctor is following things closely enough to advise you quickly if there are problems. The reality of triplets is unbelievable compared to having one baby at a time. The tough stuff is tougher and the great stuff is greater, and it starts during pregnancy. A triplet pregnancy is unbelievably stressful on the mother's body. Take care of yourself and line up whatever help you can to take care of your elder kids starting now. The 2 best things you can do for your babies right now are eat lots of protein and rest when your body suggests it.
Most OBs won't even contemplate a triplet birth other than by c/s because there are too many things that can go wrong and it is very hard to monitor triplets, especially during labour. I don't know of any OBs who would do an unmedicated, vaginal birth, because they want to be ready for a c-section if anything goes wrong. My OB was willing to consider it if I got to 36 weeks and Baby A was vertex, but only then, and she told me straight off that if anything went even slightly off, the c-section would be immediate.
You do want to make sure that even though your doctor is relatively hands off and you are very crunchy, that you are getting sufficient care. Every triplet pregnancy is different and things can go downhill very rapidly. There is good information in the Barbara Luke book and the Elizabeth Noble book about how to take care of yourself during the pregnancy to increase the chances of a long pregnancy with babes at good weights. It is worth knowing whether the babes share any of the support structures in utero because that does increase the risk.
FWIW, my story is that at 30 weeks, my OB was confident that I stood every chance to get to 36 weeks, but gave me the steroids anyway because she had lost babies in one triplet pregnancy that she hadn't managed proactively. By 33 weeks I had babies, having developed 2 different complications, each of which could have led to losing one or more babies. I now have amazing toddlers. The first year was not what I dreamed of for them, but I think it was harder for me than it was for them.
This is a great forum. glad you found us. The other place you might want to check out is the apmultiples yahoo group. I spent a lot of time there during my pregnancy - mostly lurking to get a sense of what was in store. I didn't have time for much else after the babes were born - except Karen Gromada used to hang out there and I got bfing support from her in that forum.