There are some other similar apps for the iPhone, including World Book- The Day in History and Today's History, but neither of them have as many events, and one requires an internet connection to work.
On this Day worked with no issues, but there are a few things that would make it better. Like most people, I wanted to check my birthday and see what notable events, other than my birth, took place. But the app only displays history from the current date. That's a real downer. I talked to the developer and he says he'll change that in a future version. I also found the info button with links to support and sources a bit picky about where I tap. The developer agrees, and says he'll fix it.
On this Day adds a nice feature to the iPhone, and has some real depth. I think a really nice 'blue sky' feature would be links to Wikipedia so I could learn more about these events if the mood strikes me.
Sample screens below: