In absolute numbers, there are probably more contracts executed every day that must be in writing, but there are probably more types of contracts that simply do not require writing.

In any of these types of contracts that do not require writing, you can write your terms down on paper (or memorialize them in any way you agree upon; email, napkins, etc) and still verbally execute the agreement. The writing will then become evidence of the verbal agreement.

For any specific type of contract, you will want to consult a lawyer in your jurisdiction. There is just too much variability to account for.

If your question is, "If someone gives me this written contract, and I don't sign it, but I say, 'yes, I'll do this' -- can this contract be enforced against me even if I didn't mean it and didn't sign it?"

The answer to that could very well be: Yes, you're on the hook. So don't say yes unless you mean it.

Don't ever say yes just to get out of a situation. Say, "I need to think about this for a couple of days." And if they push you, then say you're really sorry but you can't agree without thinking about it.