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I was walking around in the fields, when i stumbled upon a stone henge (much like the one's that bind armor & weapons on you for a few minutes if you accept them) that granted me a Greater Power.

So...how many of these are there in Cyrodill, where do I find them, and what greater power do they give me?

I found one, too, in the same manner. I was just walking around and touched it, and all of a sudden I could boost my agility once per day.

They are called Doomstones. They grant you with an ability that you can cast once a day, much like your innate racial ability. The stones that conjure weapons are called Runestones.

http://www.uesp.net/wiki/Oblivion:Magical_Stones

Within the Doomstones there's two types. The birthsign stones (with orange runes on them) give Greater Powers and some of them very useful, but if you first activate one and then another, you lose the power you get from the first one. I believe you have to activate them at night. Personally I stick with the Ritual Birthsign stone because it gives you Mara's Mercy (heal other 150 pts) and Mara's Milk (heal self 100 pts). When your horse is the agressive Shadowmere who loves a fight, you need it.

Then there are the Heaven Stones (red runes), and you can if you wish collect all the powers from all off the Stones. But, your combined fame/infamy has to be a certain level for each. If it isn't enough, you'll get a message something like "The hero's fate is known when the hero's fame is grown". So if you were an outright villain, they might not talk to you.