What to say when...

One of the questions I get asked the most is "What do I say when I have nothing to say?"

Yup, it seems like there is an obvious answer: say nothing.

Thinking of the various circumstances in which our minds can go blank....

1 - The big networking event.
You have an introduction (genuine - rehearsed or impromptu).  You meet some interesting folks, get past the handshake and ...suddenly... you have nothing to say.

That's ok. Listening is often better than speaking. Asking questions is easier than answering. Say nothing - get others to talk!

2 - Caught in the elevator with the big cheese (or the person you've been dying to meet)
You might have 2 floors; you might have 10. You want to make an impression but all that springs to mind is "Some weather, huh?"

Only in the movies do careers and lives get made by a fateful elevator ride.
If you have some sort of relationship already and really have something you've dreamed of pitching/offering, you could always say "So glad to run into you. I'm planning to book some time with you /hoping to take you to coffee soon. Looking forward to it." and save the subject for when you have their attention.
If you don't know each other (but wish you did) - then it's the same as standing in line at the grocery store with a stranger: smile; acknowledge them; pay a compliment/ask a question/get the ball rolling. It's not necessary to know in advance what to say; you just have to face the familiar fear of talking to a stranger.  Say something; once the door is open you will have time to think of better things to say.

3 - At a meeting where you just have no opinion
Maybe you zoned out. Maybe it's a topic that has no real impact for you. Maybe you need more time to consider options.

I'm of the opinion that if you have no opinion that's just fine. I don't get where all the pressure comes from for us to have opinions on everything. Does someone have a different opinion on this?

Saying nothing is just fine.