Guys like Rivera pitch from the right side so that right handed batters get the feeling that these pitchers’s cutters and sliders are traveling right at them. If you are a pitcher who relies on alot of laterally breaking pitches, move to the side of the rubber that is the same side of which arm you throw with. This gives your breaking pitches more illusion that they are coming at the batter (R/R, L/L), and more deception when facing the opposite side batter (R/L, L/R). And while it is generally harder to hit the outside corner from this side of the rubber, your pitches will be breaking that way anyway so it is easy to peg the outside.
If you are a guy like me though, who relies on a rising 4 Seam fastball, hard 12-6 curveball, and sinking changeup, or pitches whose action is mainly vertical, then move to the opposite side of the rubber than which ever arm you pitch with. This makes it easier to throw to the outside corner without having pitches that neccesarily break that way.
Or if you want to be really crafty, do what Trevor Hoffman does and switch sides by batter. He throws on the right side to righties, and the left to lefties. This is becuase he uses alot of middle in/off the plate in fastballs to righties to compensate for his low velocity, and his changeup just needs to be thrown low in the strikezone to be effective. Against lefties however, he tries to pound the outside corner with fastballs and backdoor sliders before using changeups over the plate or in to get them to either K or ground out weakly to the right side.