What are some interesting example of Topological spaces $X$ with the property that $\pi_1(X,x_0)$ does not depend on $x_0$?

Question

I have just started to read about fundamental groups,so my question given below may be trivial for experts.

What are some 'interesting' example of Topological spaces $X$ with the property that $\pi_1(X,x_0)$ does not depend on $x_0$ ?

I know that if the space $X$ is path connected then $\pi_1(X,x_0)$ does not depend on the choice of $x_0$.What are some other examples of the spaces with the above property?