So, yes, friction can exist in space and on other planets, but a normal acceleration is needed. In most cases that acceleration comes from gravity. For example, we can walk across the ground because our weight produces the normal force that allows the uneven surface between our feet and the ground to produce the friction needed for us to move forward.
I probably should add a clarification for "friction can exist in space" - space itself doesn't have friction - but two moving bodies in space can experience friction between them, if they make contact.