You've had them, before, and they'll happen with everyone: online and offline. Here's your chance to remember the worst awkward moment you've had to date and laugh about it. Eventually.
Edit: By request, I'm differentiating between awkward and embarrassing. The moments MUST have a situation where you can't respond in any way shape or form without making yourself seem foolish or stupid. So, really think about your moment before posting: if it was more embarrassing than awkward, try thinking of another.
Person A: "[insert conversation here]"
Person B: "That's [insert something insulting here]"
Person A: "..."
Person B: "Uh...Heh?"
I'll use my story as an example: I haven't been able to make conversations with the girl who said "Hong-Kongian" because she still remembers the comment I made all those months ago. Thus, there are moments when she refuses to speak with me if the situation doesn't call for it.