Yes, I know about triangle K... I think that is what Hebrew National Hot-Dogs has...
http://www.jewishfederations.org/page.aspx?id=71361
Yeah but Rav Abadi (former posek of Lakewood!) on his site kashrut.org says that it's kosher, it's just that some may want to keep to higher stringencies if they are completely observant and punctilious about everything else. But m'ikkar ha din (the essence of the law is the translation I guess), the hebrew national hotdogs are kosher if a person eats them, and if they are not holding at a high level in everything else, it's the least of their worries. That was the basic overview of the response on his site to queries about that.
(BTW the triangle K is run by a frum Jew (orthodox rabbi), not a conservative rabbi!)
It is a combination of politics and extra stringencies which have caused the "controversy" over hebrew national hotdogs.
As to just a letter "K" - I don't even know if that's a hashgaha at all because any company can put any letter on a box of their products, there is no trademark on just a letter, it has to have a design. So a letter K by itself means nothing.
However, some cereals which have a K, or which have no hashgaha (and no K at all) are indeed kosher, which I found listed at Rav Abadi's site, where they determine this based on the ingredients (the old-fashioned way). For instance - Fruit loops. Because there really is no need at all for certification on non-dairy, non-meat product if the ingredients are verified and known individually to be kosher. Certification is red tape in that case or a certainty so the buyer doesn't have to look up every ingredient (or post them to Rav Abadi's site, or whatever) to determine if the product is kosher.
Nowadays there are a great number of hashgaha's including half-moon-K (which is now kosher to orthodox standards), circle K, triangle K, OU, Khof-K, etc etc etc