In terms of ability, I think that Saren as a rival is a good option. They are both Spectres and in their own ways they are both trying to save the galaxy and they both actually battle each other over it. (They become reflections of one another in a similar purpose)

In terms of ideals/goals the Illusive Man is a better option. He is the machiavellian style puppet master that Shepard has to face. He in his own way embodies a view point (power/ambition/control) that Shepard has to face and consider especially towards the end. Both the Illusive Man and Anderson speak to Shepard and represent the choices she/he must make. Shepard doesn’t fight him directly, but they sort of become a duel of wills/ideals that eventually culminates toward the end of the game.

Saren (and Kai Leng - even though he wasn't mentioned in the original post) are rivals to Anderson. If you've read the books, I think you'll agree. So by default, I voted for The Illusive Man as Shepard's rival. He was a thorn in Shepard's side for two games no matter if they were working together or not.

The Catalyst

Always sort of felt like as Kai Leng did the secret dirty work for Cerberus, Shepard was tasked with the same for the Alliance. Saren was more a rival for Anderson, and the Illusive Man stood as opposite of the Alliance or Council.

The Reapers. A taste from Sovereign, who is the reveal villain in the final stretch of ME1, having been there to push characters like Saren and the matriarch down all the wrong paths. Saren is the most direct rival through most of ME1, but arguably he is not even the final boss. The necro-mecha corpse piloted by Sovereign drives home who the big bad really was, with even Saren himself not knowing the full extent of his role. Additionally, Saren’s presence fades completely after ME1, and he’s not really relevant again until the final confrontation with the Catalyst, where he can be seen as the avatar of the synthesis ending, along side TIM as control and Anderson as destroy.

Lang in ME3 is a rival, just as Saren was, but he’s finished off in the penultimate level. A milestone victory? Absolutely, but ending him does nothing to stop the overarching crisis. Killing him was probably the most cathartic, final kill of ME3, with that full blown renegade trigger being a real “fuck yeah” moment. But there’s too much at stake and too much left to do after his defeat, stopping a threat which he was not responsible for or even working for, so I would not call him the series’s primary rival.

But as the plot really kicks it into high gear with ME2, Harbinger is the closest thing to an ongoing rival. The line “assuming direct control” is burned into my head after enough playthoughs, and he really becomes the “face” of the coming storm. To me, this makes Harbinger the real standout.

Accidentally clicked the Illusive Man. I'm kind of on the fence here, since:

A) Saren is more similar to Shepard in terms of abilities and status. However, he has a lot more history with Anderson, as some people mentioned earlier. He is the first rival but not the rival in my opinion)

B) The Illusive Man is more of an ideological rival to Shepard, they have different perspectives. Nonetheless, you do work for him for almost all of ME2, and in ME3 the Reapers are the bigger threat overall. And you face TIM for the last time after his indoctrination, so he's a pawn of the Reapers at this point)

In conclusion, can't say there's the definitive rival for Shepard in the series. Reapers could be considered the overall villains of the trilogy but they're more of a giant unknowable power than a distinct personality)

If anyone's a rival it's Harbinger. He posseses the collectors throughout mass effect 2. He also takes over the minds of everyone in the arrival dlc.

Speaking of Arrival at the conclusion of the dlc. Harbinger taunts Shepard. Then there's the final push to the citadel during priority Earth. Harbinger is guarding the citadel. If your military is weak. Harbinger obliterates Shepard and the rest of the squad.