"Do Not Press", a popular interactive flash animation, is very common among the internet. Many profiles or signatures on the web include a link to this application.

The animation starts by showing a large red button that says "DO NOT PRESS." If you click it, you get a half-hour long story that ends up repeating itself once you reach the end. People enjoyed spreading the lulz, so they posted links to the button all over their accounts and forums- and eventually made their own jokes involving red buttons, like "Soul Stealer" or "Rick Roll" links.

Examples:
Press this. I dare you.
Don't click this!

"Do not press" didn't necessarily start the red button jokes, but it was certainly a large part of them.

More "Do Not Press" applications became available for the iPhone/iTouch, including the original, to continue the lulz and spread them around.

Here is a link to the application.

Here is a video of the application.

Google Search Trends for:
Do not press Do not press the red button

B marks the release date for the iPhone app.