Hard boiled eggs outside the fridge
This is kind of a holy war question, oddly. The official party line is "Two hours, just like any other food" but there has been an informal and impromptu Easter-driven experiment in progress for the last two-thousand years or so which most people have participated in and which argues strongly against the hard two hour rule. This doesn't mean the two hour rule is wrong: it's just really conservative.

In a nutshell, cooked solid protein tends to be quite resistant to bacterial contamination. Historically, cooked meat was stored for days with a low (but non-zero) chance of significant contamination. Even today, raw meat is "aged" for several weeks in some circumstances without ill effects.

So yea, it's probably not going to kill you, but if you want to be 100% safe, you should stick to two hours. If you're willing to take some risk, use your senses. Eggs stink when they start to go off, and the human nose is very sensitive to spoilage.