Consider, for example, these different scenarios:
One partner, upon being offered an entry-level tenure-track job, negotiates a non-tenure track job for the other
Someone already in a TT job negotiates a non-TT job for his or her partner
One partner is already in a TT job and the department creates a TT line for his or her partner
Two partners apply and get hired for two TT jobs in the same department at the same time
Two partners get recruited and hired for two TT jobs together
One partner, upon being recruited for a senior position, is offered a second TT position for his or her partner.
One partner, already in a TT job, gets an outside offer, and makes a TT job for his or her partner a condition of staying
One partner is already in a TT job, the department runs a search for a TT position in the other partner's field, and that partner gets hired after a national search
One partner is already in a TT job, the department has an opening in the other partner's field, and hires the other partner without a national search
All of those are situations that get described as "partner hiring," but they're quite different. Generally, when I talk about partner hiring, I mean situations where each partner ends up in a tenure-line job at the same institution--both because I presume that, all other things being equal, most couples would prefer that scenario, and because it's the filling or creating of TT lines that causes the most trouble and potential conflict.
However, even with that limitation, there are still so many variables that I'm not sure it's even possible to talk about "being in favor of" or "being opposed to" partner hiring in general.
Since I'm part of an academic couple and I know many others, I've always previously said that I support partner hiring. But when I say that, I'm taking as a given that both partners are accomplished and desirable hires, and more than competitive within the pool of other applicants (or relative to other recent hires); I'm also assuming that no one is forcing anything on a hiring department--that, if there wasn't a national search, there was at least a consensus that hiring the partner was a smart pick-up. That reflects the scenarios I know best: situations where both partners are on the tenure track at peer institutions, producing work basically equivalent in quantity and quality, but for whom finding jobs at the same place remains elusive.
Those who dislike the idea of partner hires often have a very different scenario in mind, sometimes equally born of unfortunate personal experience: a less-qualified partner gets hired, without full departmental consultation, sometimes as the result of one or two people throwing their weight around, and sometimes in ways that reinforce traditional power structures (senior man gets his 25-year-old girlfriend hired; straight people get privileged over queers; chair or dean makes an executive decision).
I'd venture to say that, phrased that way, almost of us are in favor of a good opportunity hire who's committed to the institution because it's where his or her partner works and against an underqualified hire that's forced upon a department--and if those distinctions are more than matters of perception, they come down partly to institutional type and culture. A less-healthy institution is more likely to do partner hiring badly (because the culture is an imperial one, or where certain kinds of people get valued more than others), and a more healthy one is more likely to do it well or at least in ways that don't piss other faculty off.
If I could propose a few general rules, though, these would be they:
1. Any secondarily-hired partner should be competitive within the department's usual pool of applicants. It's foolish to say that he or she must be the most qualified person (since the idea that one can rank candidates in some absolute and objective way is usually a fiction), but he or she should do more than meet minima.
2. The decision to hire should be made in a way that has widespread departmental support, whatever that might mean in a given context.
3. If hiring a partner means creating a new line, it shouldn't compromise existing hiring goals (e.g., hiring another Americanist shouldn't mean foregoing the medievalist a department has been requesting for three years)
4. No preference should be given to straight couples over gay ones
5. After hiring, the partners are expected to function as independent agents, getting no preferential treatment and each doing his or her fair share of service. (The exception would be cases where two partners are hired to share one line.)
None of this, however, makes actually attaining a partner hire any easier, and it's harder the earlier one is in one's career and the less leverage one has--I know virtually no one, for example, who upon being offered an entry-level tenure-track job was able to negotiate a second TT job for his or her partner. And none of this protects a department against disaster scenarios like a messy divorce.
The real problem, for everyone, is that partner hiring is no one thing, and it's hard to make a general rule or take other people's experiences as either a model or a warning.
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Readers, what would you add to my list? Or do you have any advice either for those trying to solve the two-body problem or departments considering helping them?

