But few of those characters can accomplish such great feats even with jumping, running , ground pounding and punching/kicking. Mario is one of the few who can get by with just these things and still kick total ***
Actually, a lot of characters can take advantage of those basic moves. For instance, Sonic can do more than Mario can, even if he's limited to those actions; he does them all better.
His Spin Jump attacks all angles rather than only those below him, and he can channel his speed to jump extremely far.
He runs faster, of course, and he can Boost into opponents by creating an aura around him while running.
His Stomp comes out instantly, as opposed to Mario's little flip he does. Also, he has a bouncing variation.
He punches/kicks faster, which fits with his general "speedy" nature.
Also, Samus can wall jump infinitely on a single wall. Just something that came to mind.