This question is interesting, as it does not ask: How does YOGA benefit you, but how has ASHTANGA YOGA benefited you? I am going to answer it precisely like that, even though I continue to benefit from Yoga in general and Ashtanga Yoga in particular.
So far, Ashtanga Yoga has benefited me in the following ways:
On a physical level, I have become much stronger than I have ever been. I used to have very weak arms and shoulders. This has changed thanks to the Ashtanga Yoga Primary series which is known for building strength there paricularly. But I have also become much more toned in general. It was never my intention to lose weight by practicing Yoga, but it has clearly happened. Thanks to practicing Ashtanga Yoga up to six times a week - less at present, unfortunately, because I currently struggle with afternoon migraines - my stomach seems to have become this black hole that I can just throw tons of food into and it will make them disappear. When I don’t practice as much, my metabolism slows down and I gain a little weight back. A very logical and normal cycle. Also, thanks to Ashtanga Yoga, I was able to partake in 6km run a few moths ago without any kind of further cardio training. It took me 35 minutes or so to reach the finish line, but for someone who hasn’t trained once, that’s pretty good I think.
On a mental level, Ashtanga Yoga has helped me calm down and relax. I can now sit and meditate for a while (albeit never longer than 20 minutes), which was unthinkable a couple of years back because I have been diagnosed with a milder form of ADD in my teens. Thanks to Yoga in general and especially the routines of Ashtanga Yoga in particular, I have that under control now. Also, I know that lots of sun salutations and down dogs in particular can help with symptoms of depression. So whenever I feel a little down or lethargic, I throw in a couple of rounds of Surya Namaskara. Asthanga Yoga has also taught me discipline, modesty, patience and dedication. It has made me interested in health issues and physiology, and in that broadened my horizon and outlook on life.
These are just a few points that spontaneously come to mind after one year of Ashtanga Yoga. I’m sure I could come up with even more benefits as I continue to learn so many things about life and myself. Ask me again in a year and we will see what I can say then! ;)