I'd also like to add a couple of other feuds that would probably be awesome: The Shield vs The NWO and Steve Austin vs Jake Roberts.
The NWO and The Shield are easy to draw parallels to one another - both are trios, both have the gang-mentality of using strength in numbers to surround their prey before they go in for the kill and demolish them, both groups have a big man enforcer (Kevin Nash for the NWO, Roman Reigns for The Shield), etc. You know those moments during tag team matches where one man gets tagged in but wants the other legal man to tag in a partner of his because he wants a piece of that other guy instead? I imagine a cool moment like that between Roman Reigns and Kevin Nash. They're both the biggest dogs in this fight and they want to get into the ring with one another for the first time to see who the biggest dog in the yard really is (I imagine the moment where they step to-to-toe with each other would be received with a big reaction.) A lot of cool things I can think up for this rivalry, if only Hogan/Hall/Nash were at least as young and in shape as they were during their 2002 run...
Steve Austin and Jake Roberts would be a interesting rivalry for similar reasons, which is the fact that there's parallels between the two men. Both men are "snakes", neither man can be completely trusted, both can be cold blooded when the situation calls for it, etc. Austin's old motto is "D.T.A... Don't Trust Anybody" and Jake's second theme as a heel from 1991-1992 was "Trust Me" (my favorite theme of his), which was his devious way of saying he couldn't be trusted. I picture this feud starting up because the two become tag team partners on one special occasion (no idea why) and Roberts ends up turning on Austin for some reason. He then cuts a promo in his usual eloquent way, talking about how a man like Austin should know better than to trust a snake. Seeing Roberts play mind games with Austin would be great. Plus, both men's style of punching and kicking and striking blows on their opponents is pretty similar, so I picture just an all-out brawl and "slobber-knocker" (as JR would put it) when they two stepped into the ring with one another.