Country Squares: Post introduced "Country Squares" in 1963.
Pop-Tarts: Kellogg's quickly developed their own version, the now ubiquitous Pop-Tart, and released it in 1964. 
Toastettes: Nabisco (which is now owned by Kraft Foods) created their own toaster pastry called "Toastettes", to compete with Kellogg's Pop-Tarts. The brand, can be dated to 1967, were discontinued in 2002 after a failed marketing effort to tie Toastettes in with Nabisco's children's brands. Nabisco also made a toaster pastry based on the Oreo cookie as "Kool Stuf", which was also later discontinued.
Toast'em Pop-Ups: Another competitor with Pop Tarts, "Toast'em Pop Ups," survives. Toast'ems began production in 1964 under a General Foods [Post] contract with the Schulze and Burch Biscuit Company and were the first toaster pastry - unveiled in Feb. 1964 as Post "Country Squares" and changed in 1965 to Toast'em Pop-Ups. The company reacquired the rights to Toast'ems in 1971.
Toaster Strudels: Pillsbury's Toaster Strudel is a toaster pastry meant to taste like a traditional Germanstrudel with icing. The icing comes in a removable plastic package, and the pastries must be frozen, unlike other toaster pastries.