It now appears very likely that Moammar Qaddafi was killed at the hands of his captors. Human rights groups are calling for an inquiry and the International Criminal Court has reportedly asked to examine the former leader's body (it's not at all clear that the Libyan authorities will acquiesce to that request). The question that is already arising is whether Qaddafi's killing constituted a war crime that could be investigated by the ICC. The answer, in short: Yes, it was likely a war crime; and no, the ICC is not likely to prosecute anyone for it.
First, the question of whether Qaddafi's execution constitutes a war crime that falls under the ICC's jurisdiction. To be a war crime, there's got to be a war (or state of armed conflict). Here, there's no doubt that there was an armed conflict underway when Qaddafi was killed. Does killing a combatant who has surrendered constitute a crime? Quite clearly. The ICC statute includes in its list of war crimes the following:
Killing or wounding a combatant who, having laid down his arms or having no longer means of defence, has surrendered at discretion...
What's more, the ICC's jurisdiction over crimes committed in Libya extends to the actions of the NTC and anti-Qaddafi fighters just as it does to Qaddafi's own men. The Security Council referred the "situation" in Libya to the court, not the particular behavior of one party or another.
But the fact that the ICC would have jurisdiction over Qaddafi's killing does not answer the question of whether it's likely to investigate. The court has no obligation to prosecute all or even most of the crimes that fall under its jurisdiction. In fact, the ICC's governing statute clearly guides the prosecutor away from isolated acts toward large-scale behavior:
The Court shall have jurisdiction in respect of war crimes in particular when
committed as part of a plan or policy or as part of a large-scale commission of such
crimes. [my italics]
The choices of the prosecutor and the rulings of the ICC judges in recent years have made abundantly clear that the court prioritizes large-scale crimes that form part of a broad pattern or practice. Given that emphasis, it is unlikely the court will ultimately prosecute anyone for Qaddafi's killing unless they decide that there existed within the anti-Qaddafi forces a broad practice of war crimes or crimes against humanity and that the Qaddafi killing was a manifestation of that.
What's more, the new Libyan authorities could foil any ICC investigation by carrying out their own investigation. With a national investigation underway, the ICC must yield unless it determines that the investigation is a sham. To the chagrin of many (mostly outside Libya, it seems), Qaddafi will never now see a courtroom in the Hague; neither will whoever killed him.
From the comments: Kevin Jon Heller, who knows as much about the ICC as anyone, believes an investigation into the killing is possible:
Although I share your skepticism that Gaddafi's executioner will ever face prosecution, I don't think the odds are quite as bad as you claim. Don't forget, although the Security Council's Darfur referral was directed at the actions of Bashir's government, not at rebel groups like JEM, Moreno-Ocampo nevertheless brought charges against rebel leaders for their alleged involvement in the murder of 12 Blue Helmets. That was an isolated act, yet Moreno-Ocampo had no hesitation in pursuing it. (And it's important to note, though it's implicit in your post, that the "plan or policy" element is not jurisdictional; it's little more than a suggestion.) Is it really inconceivable that Moreno-Ocampo would charge the murder of Gaddafi along with various crimes committed by the Gaddafi regime? After all, his rebelphilia is legendary...