Why is the Moduli of smooth curves of a fixed genus not compact/proper?

I know that there is a compactification using stable curves. But is it easy to see that the Moduli of smooth curves is not compact?

Following Sam Need's comment, I should write that I am comfortable with the Moduli of smooth projective curves i.e., as an algebraic variety.

intuition, if you have some moduli space which parameterizes objects which can degenerate to an object outside the class you're dealing with, then this indicates the moduli space is not compact. $\endgroup$