An interesting question was raised in the comments section of one of the posts: Who, exactly, are the Suns rivals?
One could consider any member of the Pacific Division or Western Conference a rival, but that seems a little broad, especially considering the disparity in talent levels or lack of proximity involved. That would certainly seem to dilute the impact of any one rivalry.
You could then cut that number down to say, the top half of the Western Conference and Pacific Divison since the Suns have been playoff contenders for most of their history and therefore are constantly jostling with the top teams in the conference and division for playoff seeding.
And then you can look at history and say the Suns have met the Spurs and Lakers pretty frequently in the playoffs and even their regular season games have a playoff vibe to them. Of course, the problem there is that historically, both the Lakers and the Spurs have more or less pwned the Suns so those rivalries would seem to be a bit one-sided (see Red Sox vs. Yankees, 1919-2003). Technically speaking, this would make the Lakers and Spurs more nemeses (from Merriam-Webster.com: a formidable and usually victorious opponent or rival) than rivals.
Regardless of that history, the respective fanbases of the Suns, Spurs, and Lakers definitely get fired up for those games: Suns fans because they resent the success of the Spurs and Lakers (hence the habitual reference to the Lakers and Spurs as cheaters, floppers, bores, David Stern's favorites and other insinuations that neither franchise has "earned" its success) and hold a burning desire to upend the Western Conference power structure; and Spurs and Lakers fans because they consider the Suns inferior never-was also-rans (hence the habitual reference to the Suns as whiners, crybabies, excuse-makers, conspiracy theorists and other insinuations that the Suns haven't earned a seat at the grown-ups' table, i.e, won a ring) and so they can break our hearts one more time.
That said, I'd also include the Mavericks here since they are most like the Suns in their inability to get to the promised land, yet consistently flirt with the ultimate success that both the Lakers and Spurs have achieved in recent memory. The Suns-Mavs history has been a rivalry of scraps so to speak. (Oh and there was that one time Danny Fortson committed a flagrant foul on Zarko Cabarkapa and broke his wrist... never forget!)
As for me, I think a Suns win is a Suns win. If it's against a Western Conference team (especially a top one like the Nuggets or Jazz), that's good because it helps with playoff seeding. If it's a Pacific Division team, even better because it put the Suns one step closer to winning the division and guaranteeing a top seed. Against the Mavericks? That's a nice measuring stick with regards to the top half of the Western Conference. And if it's against the Lakers or Spurs? Well, that's one step closer to the grown-ups' table now, isn't it?