Does posting a link to a copyrighted file, such that accessing the linked file would constitute infringement, but where the file itself is not on my servers, constitute any sort of crime or infringement?
In Canada, no: linking does not reproduce any part of the original.
In the US, it isn't as clear, but generally, linking is not per se infringement, usually because no copying happens.
Posting one link is, by itself, unlikely to constitute copyright infringement in most jurisdictions (see nomen agentis's answer). But posting a lot of links, systematically and with emphasis on making it easy for people to find content known to be pirated, is an entirely different situation, and you should consult a lawyer before trying it.
It is well established that creating a repository of P2P content which is substantially piratical is contributory copyright infringement, even if you never host anything copyrighted. Take out the "P2P" and you've got a scaled-up version of what OP describes. I find it hard to believe that P2P technology is the key point of these rulings. This is about what you are doing, not how you go about doing it. If the primary purpose of your website is helping people commit copyright infringement, it is unlikely you will be able to effectively defend yourself in court, regardless of the specific technology in use.
In the US, knowingly and intentionally linking to infringing copyrighted material may be held liable as contributory infringement.
You should not expect that claiming you were merely linking to the material but not hosting it directly yourself will automatically remove you from all or even any liability if a case is pursued.
I won't get into the likelihood of your being pursued or not for said inducement if it is only a single link (and depending on the nature of the linking/surrounding context): retain an attorney if you want specific advice related to that. While I would personally find it surprising, there are many civil suits or threats of civil suits in particular that occur under more "surprising" circumstances: it's certainly possible.
While the copyright statutes do not contain language specifying contributory infringement or express a given remedy, there is case law related to it that establishes it in a way very similar to contributory infringement under patent law.
In particular the supreme court decision in Metro-Goldwyn-Mayer Studios Inc. v. Grokster, Ltd., 545 U.S. 913 (2005), of note:
We hold that one who distributes a device with the object of promoting its use to infringe copyright, as shown by clear expression or other affirmative steps taken to foster infringement, is liable for the resulting acts of infringement by third parties.
and it's also worth paying attention to how they look at the relationship between patent law (which does have an inducement rule) and copyright for the purposes of the decision:
For the same reasons that Sony took the staple-article doctrine of patent law as a model for its copyright safe-harbor rule, the inducement rule, too, is a sensible one for copyright. We adopt it here, holding that one who distributes a device with the object of promoting its use to infringe copyright, as shown by clear expression or other affirmative steps taken to foster infringement, is liable for the resulting acts of infringement by third parties.
Particularly, consider how the court chose to look at evidence of intent and the relation to inducement:
[t]he rule on inducement of infringement as developed in the early cases is no different today. Evidence of "active steps ... taken to encourage direct infringement," Oak Industries, Inc. v. Zenith Electronics Corp., 697 F.Supp. 988, 992 (N.D.Ill.1988), such as advertising an infringing use or instructing how to engage in an infringing use, show an affirmative intent that the product be used to infringe, and a showing that infringement was encouraged overcomes the law's reluctance to find liability when a defendant merely sells a commercial product suitable for some lawful use.
and consider that in Sony Corp. v. Universal City Studios, Inc., 464 U.S. 417 (1984) the key to ruling in favor of Sony Corp was the conclusion that the Betamax was capable of significant noninfringing use.
The question is thus whether the Betamax is capable of commercially significant noninfringing uses
The Digital Media Law Project gives its definition as
Contributory copyright infringement occurs by "intentionally inducing or encouraging direct infringement" of a copyrighted work.
and may have some relevant further reading.
If users of a site you administer (versus you yourself individually) are posting links to infringing material, you may have some protection under the DMCA assuming you correctly follow related requirements (particularly re: takedown procedures) correctly and assuming the primary purpose of the site being administered is not seen to be infringing or contributing to infringement.
While I believe it to be untested so far (?), the DMCA safe harbor specifically addresses user action, but does not address a case like that of Grokster if the court were to find that the primary purpose of the site overall were contributory infringement. If anyone is aware of any related rulings that specifically address this in relation to the DMCA, I'd love to see them.
(some might point to MegaUpload/Kim Dotcom as possibly being related to this last, but that is far too controversial and with too many other prevailing issues to be worth citing, nor has it been decided at an appropriate level.)