With no till, you rely on freeze/thaw (heaving) and earth worms to rebuild soil structure. It really works...really. When we plowed and disced years ago, we would have "concrete" by the following year. 2 or 3 years without tillage, and I can literally dig down deeper than we ever plowed and find nice mellow soil structure. 20+ years and the ground absorbs rain like a sponge, is mellow, and it's more productive. No tilled ground doesn't suffer from the same compaction woes as ground that's frequently worked. We don't need as much weight on the tractor since we aren't doing tillage, and we make quite a few less pass's across the fields, compaction in minimalized even further.
With any tillage tool, you create layers where soil density changes at the depth you run them. Corn in particular will root to that depth, then start spreading parallel with the surface. The roots simply take the path of least resistance. With no till, you don't have that change in density. Crops will continue to root deeper. That's a major + in drought conditions.
Not all soil works as well, and not all climates support no tilling. But make a commitment to the process and it definately works. Do it right and yields INCREASE, fuel cost DECREASES, time and equipment cost drops, and soil stays where it's supposed to be. With the savings in time, we farm 3 times the ground now as we did in the "old days". And that's with smaller tractors (that use WAY less fuel)
When I first started no tilling, I had my doubts. First year, most doubts were removed. By year 2 or 3, I sent my tillage tools to the sale barn. You couldn't pay me to spend hour upon hour dragging a plow around these days.
Google "plow pan" and get a detailed explaination of why moldboard plows create a compaction layer. That's the biggest single reason why moldboard plows fell from popularity years ago. Still some instances where they have a niche.