Well, usually there's a sort of "fallback guy" that wrestlers who make it big can frequently feud with over and over again and it (for some reason) doesn't get old. Sometimes its a weird "feud triangle" in a way as they can team up at times and feud at other times.
EXAMPLES:
Austin/Rock and Rock/HHH
Hart/HBK and HBK/HHH
Big Show/Undertaker/Kane
And it appears as though there are a few new examples of this that are brewing...
Ever since Benoit's departure, we've seen countless Morrison/Punk matchups. The two of them appear to be fusing into a feud similar to the likes of Rock/HHH when they were in the upper midcard range.
Its much too early to guess where the likes of Rhodes, DiBiase, Bourne, Kingston, Miz, and the other young talent will go. And there are some guys that just never found that niche. Batista really doesn't have an "archenemy", does he? Neither does Edge, surprisingly.
This thread brings up the concept of Orton's rival. Well, there's no other choice but John Cena. These two are going to be around for a long, long time, barring some unforeseen circumstances. They've got virtually the same track record, they're pretty evenly matched when it comes to the look and their presence, but they also have that sort of "brotherly conflict" aura around them. Writers tend to make the hero (in this case, John Cena) rivals with someone that could very likely be their greatest ally if it wasn't for one major flaw. Some would think that Cena being a guy who stands up to a challenge means that he should feud with someone who backs away and runs like a coward, as that's contrast, but in actuality, the more interesting feud is with the guy who reciprocates said confidence. Orton's heel isn't like that of MVP or Kendrick or even Edge at times. He isn't the coward. He's the disrespectful and arrogant guy who can get the job done by himself. So while Cena brings "loyal but lonesome" to the table, Orton brings "selfish but surrounded". Orton can get the job done on his own but will frequently bend the rules or flat-out break them just for the pure sake of getting away with it, while Cena will stay true to the foundations and when he does win, it means that much more because he wasn't facing someone that was inadequate. A hero isn't admirable if he destroys someone half as skilled as he is. He's only cheered if he overcomes a greater threat. Two people that are evenly matched, but one willing to cheat to gain the upperhand is more of a threat than a coward who needs the equivalent of a bazooka to win a fist fight.
Maybe its just the writer in me getting out, but that's how I see it. Orton/Cena will be feuding for a long while, and it seems very clear that those two will be the ones syncing up, so really, the more interesting question is....who will be Edge's?