Here is a list of data-mined feats of strength thus far: http://d3db.com/achievement/?c=5505067#1-1-0
They fall into several categories: "One of the Chosen" - Participated in the Diablo 3 closed beta Participated in the web promotion for each class (earning the sigils by creating banners)
"Discriminating Taste" - Bought the Collector's Edition "
In the Land of Killer Unicorns" - Get to the secret non-cow level for ideas "Kill the unburied Jay Wilson"
- Kill a monster named after D3's Game Director, in a special secret dungeon
gaming.stackexchange.com/users/3241/Wikwocket
"One of the Chosen" is the only Feat of Strength that has been discovered so far, to my knowledge.
It is the Feat of Strength given to players that were in the closed beta.
gaming.stackexchange.com/users/7494/Klokworkk
I also did all five class web promotions during the pre-release of the game.
Blizzard took their while to grant these but they're all in my account now.
They're named: "Brushed up on the Barb" for the barbarian
"Wise to the Wizard" "Delved into the Demon Hunter" "Witch Doctor discovered" "Mindful of the Monk"
All were credited on the 28th of June (at least for me)
gaming.stackexchange.com/users/29249/Worf
"Kill the unburied Jay Wilson" got this one, and its title is "Smash!
Jay, smash!"
Its a secret level in one of the crypts, when doing the black kings crown in the cemetary.when
you enter the crypt changes its name to "developers hell" and all the mobs are, well, developers...
Zombies with names of people working on D3...
And the boss is none other than Jay Wilson!
gaming.stackexchange.com/users/25445/Aql
In the land of Killer Unicorns is another feat of strength got it on the 18th
gaming.stackexchange.com/users/25715/Tyler
I've gotten 3 so far.
D3 Collector's Edition Killing the Unburied Jay Wilson in Developer Hell (random 4th dungeon at the crypts in Nightmare or higher) Finding Whimseyshire (secret unicorn/rainbow level)
As far as the exclusive sigils go, I've not seen anything from Blizzard yet on these.
I did all 5, have the emails as proof and time stamps but do not have them on my account.
gaming.stackexchange.com/users/27008/Byron
Like the title says - what are the known feats of strength in the game?
What are the feats of strength in Diablo 3?
gaming.stackexchange.com
<diablo-3><achievements>
gaming.stackexchange.com/questions/66748
gaming.stackexchange.com/users/25398/Nevir
They fall into several categories: One of the Chosen, Discriminating Taste, Land of the Killer Unicorns, Brushed up on the Barb. It seems that feats of strength is some kind of an achievement list. 
The community is offering details, regarding the feats of strenght, based on personal experiences.