"Dare" with and without "to"

To my surprise, there's a missing question about this particularly interesting verb, dare. All I know about it is the fact it can be in two forms, as an auxiliary (without to: "I dare not mention their names") and main (with to: "Did anyone dare to admit it?") verb and the difference has something to do with agreeing with subject. Can somebody explain in a greater detail?

Dare is a semi-modal verb. The speaker can choose whether to use the auxiliary "to" when forming negative and interrogative sentences. For example, "I don't dare (to) go" and "I dare not go" are both correct. Similarly "Dare you go?" and "Do you dare (to) go?" are both correct.

Taken from the Wiktionary.

Note that when dare means challenge, it requires to, as in:

I challenge you to ask her out.

I dare you to ask her out.