Given this state of affairs, please consider first reading this before continuing, and - for anyone who's experienced rape or indecent assault - be aware that the following discussion may include triggers.
First, a caveatThere's an almost-omnipresent meme in society today, that rape is entirely or primarily about power. It's one of those incredibly hardy, robust memes that are simultaneously difficult to argue against without leaving yourself open to accusations of apologism, or excusing the inexcusable (see also: civil rights for captured terrorists, differentiating between child molesters and paedophiles, etc), which likely accounts in no small measure for its widespread success.
With that in mind, nothing in this post should be taken to excuse, diminish, apologise for or trivialise rape or rapists. Rape is a hideous, inexcusable phenomenon, and should rightly be viewed as such. However, that doesn't excuse inaccuracies or inconsistencies in its characterisation or people's beliefs, and pointing them out does not diminish its evil in any way. Moreover, with a more accurate understanding of the problem one can almost always fight it better.
In summary: one can still believe Hitler was a monster without having to believe he also had horns and a tail. Moreover, WWII would have gone significantly more poorly for the allies if we fell into this trap and allowed ourselves to believe the Nazis could be beaten with a Bibles, silver and holy water.
That said (and hopefully any offended sensibilities or jerking knees pre-emptively defused), on with the discussion...
Problems with the "rape=power" memeThe primary problem with the "rape = power" meme is that as far as I can tell it is completely and utterly unsupported.
That sounds incredible - at first - given its prevalence, but I've researched this quite heavily, and I am literally unable to come up with a single evidence-based source for the claim. Literally the closest I've been able to find for a source for this claim was a 1974 documentary about violence against women, wherein a group of prisoners who formed an organisation named "Men Against Rape" in Lorton Prison were interviewed regarding attitudes to rape.
In this documentary the prisoners claimed (apparently without evidential support) that male-male rape in prisons was primarily a power relationship, and then baselessly hypothesised that the same might hold true for all rapes, outside of the kind of violent, criminal, uncivilised, exclusively-male, strongly hierarchical, macho culture that characterises prison life.
Aside from the highly speculative and unsupported basis of this claim, it's also worth knowing that of this group, only one of their number was even a convicted rapist.
Got that? We have a bunch of unqualified prisoners, only one of whom is even part of the group they're hypothesising about, suggesting that rape in their particular prison is primarily a power issue, and generalising from that not only to "all prisons", but to all rapes. Hmmm.
Moreover, despite the fact the claims were speculative, unsupported, advanced by completely unqualified individuals and of dubious applicability to life outside prison, they were picked up and quickly became society's default assumption as to the nature of rape. An assertion with which, moreover, even the makers of the documentary seem to have something of an issue (read the last post on that page).
In addition to a fundamental lack of supporting evidence, there are also several empirical factors that appear to counter-indicate the idea that rape is primarily or entirely a power relationship, and has nothing to do with "normal" sexual attraction:
To begin with - even controlling for extraneous factors like socialising patterns, socio-economic level and the like - rape victimisation is hugely more common amongst younger people than older. Were it simply a power relationship one would expect no significant difference between ages, or even (outside childhood, wherein child abuse is a related but distinct phenomenon) an increased likelihood with age, as ill-health, infirmity, mobility problems and/or dependency on others all increased, and the individual generally presented an easier, more tempting target.
There are also several scientific studies demonstrating that as access to pornography goes up, rape goes down. It's hard to imagine how rape can be primarily about power and not about satisfying sexual urges, when improving individuals' ability to satisfy sexual urges leads to a measurable reduction in rape (and, note, in no other type of violent crime).
In addition to this, there are plenty of documented instances of forced or otherwise coercive sex in the animal kingdom. I'm somewhat leery of evolutionary-psychology due to its inherent non-falsifiability, but when you have a behaviour - that's commonly asserted to be about a conscious lust for power - being demonstrated as a successful reproductive strategy even by non-conscious animals, I think we have to acknowledge that - distasteful though the activity may be - there's at least some chance that it's simply an evolved reproductive strategy (ie, an instinctive satisfaction of sexual/reproductive urges) rather than purely a psychosocial dominance issue or power-play.
Finally, the word "rape" covers a multitude of sins. Statutory rape is rape. Date-rape is rape. Even drunk mutually-consensual sex can be considered rape if one partner later decides they regret it.
Violent, sober, non-consensual sex is a horrifying phenomenon, but in our society "rape" is not always necessarily the same thing as "violent, sober, non-consensual sex". In particular it seems... problematic to reasonably argue that an overly-insistent drunken hookup, a 17 year-old sleeping with a 15 year-old that they're in a long-term relationship with and a violent alleyway sexual assault at knifepoint are all committed by offenders with exactly the same psychological type, with exactly the same motivation.
Upon reflection, it's not so surprising that there's no hard evidence supporting this assertion - dealing, as it does, with intangible and subjective psychological motivations that you can't empirically test. The question is, then, given all the evidence against it and the paucity of evidence in favour of it, how did we as a society ever get so convinced of it?
So why is it so enduring?From here on in I'm hypothesising rather than reporting documented history or scientific conclusions, but I suspect it's because such a view of rape demonises and de-humanises rapists, so it's more appealing to many members of both sexes.
To many "old fashioned" feminists or people strongly interested in women's issues it suggests by association that all men are at least potentially insatiable power-hungry oppressors with unnatural, destructive motivations, and it casts the penis as the weapon of the oppressor. Modern (third-wave) feminism has right moved away from this kind of misandrist rhetoric, but it was a lot more common in the past, and flattering this kind of world-view would certainly account for why the meme became so popular when it did, especially given feminism (as an institution) has been primarily responsible for pushing the issue of rape into the public eye (and rightly so).
Equally, to many men (even ones uninterested in women's issues) it allows us to characterise rapists as some violent, power-obsessed "other". We've all been horny and drunk or otherwise impaired, but we've never raped anyone. If plenty of rapists are just guys with normal sexual urges and a little less self-control than us it's deeply unnerving, as it suggests that - in the right situation - we could potentially do something like that. Casting rapists instead as power-mad abusers with no normal human motivations is therefore more comforting to us, as it's a rigid separation stopping "us" from ever becoming one of "them".
It's the same idiotic cartoon-o-vision mentality that says paedophiles (people with a sexual orientation who have no choice over how they feel) are all uncontrollable child molesters (people who choose to give into their urges and perform an action), or that terrorists like Osama bin Laden are all necessarily two-dimensional, moustache-twirling megalomaniacs who sacrifice their lives in attacking western countries simply because they hate every single individual in the country because of their "freedom"... rather than people who are legitimately angry about the effects of western countries' foreign policy on their regions and their families/friends, and who - lacking any conventional ability to effect change - instead out of desperation choose tactics which we find morally abhorrent.
In short, we overwhelmingly and unthinkingly believe this as a society not because it's empirically proven, or supported by evidence, or even particularly plausible. We apparently believe it purely and simply because it flatters our preconceptions and makes us feel better about ourselves... and that's no reason to believe anything.
So now we've cleared that up, while we continue condemning rapists and rape, can we finally put this tired, baseless, inaccurate, misleading, counter-productive meme to bed?
Footnotes Given the hot-button nature of the subject, lest anyone be inclined to jump to assumptions regarding a pro-rape or "mens-rights" agenda on the part of the linked blog article, bear in mind that it's written by a blogger dedicated to sex-positive feminism.
 This paper separated adult rape victims into seven age-bands (18 to 24 years, 25 to 29 years, 30 to 34 years, 35 to 44 years, 45 to 54 years, 55 to 59 years and 60 years and over). After controlling for all other factors, the analysis indicated that each successive band has only around a 70% of the risk of the previous band of experiencing rape. In other words, compared to an 18-24 year-old, a 45-54 year-old is only 24% as likely to be raped.
Similarly, this paper reports that outside of the ages 12-15 (which include child abuse - a related but distinct problem to adult rape), you are at most risk between the ages of 20-34 (0.9/100,000 people), then 16-19 (0.6), then 35-49, then 50-64, and last of all 65 or older. Aside from the (already-mentioned) child-abuse outlier, this clearly shows a correlation between the ages when people are commonly considered most attractive, and next to nothing about vulnerability or opportunity for dominance.
 There is , it must be acknowledged, also an egregious gender-imbalance in this particular case, but that's a whole other discussion, equally inflammatory and controversial in its own right.