While I'm not one to hate on shounen (I enjoy all four demographics), there's no arguing the fact that the tropes typical to the demographic greatly limit originality and opportunities for character development. Shirodaira Kyou, however, has managed to utilise the typical themes of willpower, hard work and friendship to create a fairly intricate plot which, while extremely infeasible from a real-life standpoint, is intriguing both philosophically and logically. While certainly not a masterpiece, and despite leaving several minor loose ends at its conclusion, Spiral - Suiri no Kizuna is one of the better manga in the psychological + mystery genre, with a fairly likeable cast and mind games that are complicated enough to hold your attention while not venturing into "ridiculously convoluted" territory.
That said, there are numerous complaints about this series, some of which I'll address here for the benefit of future readers:
nakie08 : Characters are nonchalant about death -- A strange comment considering the entirety of the plot hinges on Ayumu trying to find a way to circumvent fate and avoid killing the Blade Children, and how at the conclusion, most significant characters are shown going on journeys specifically to atone for the lives they've destroyed. Admittedly, many of the murders that do occur aren't met with lamentation on the part of the survivors, but considering their biological makeup and upbringing, that's hardly surprising. Which this commenter would have known if he'd bothered to read past the first few volumes. (And really, using Majin Tantei Nougami Neuro, which is chock-full of black humour, as an example of a manga that treats life more respectfully than Spiral? Bizarre)
songofthewaves : Pseudoscientific, religious hogwash -- Sci-fi is, in fact, one of the genres; and since the "science" in practically every work of science fiction ever created is pseudoscience, the first part of this complaint can be resolved simply by looking at the genre and category tags before reading to make sure you aren't taking on anything you don't like. There is a religious element to the plot, but, as is explicitly stated in the manga itself: whether God and the Devil exist or not doesn't matter; what matters is whether people believe in it and act according to what they think is "God's plan" or "the Devil's will." While atheism has been the in-thing these past couple of decades, the power of religious faith - in the sense that if you believe in something strongly enough it can have a profound effect on your actions and lifestyle choices - is undeniable, and that's what Spiral attempts to deal with. As even most seinen mangaka would be unable to tackle this topic successfully, Shirodaira Kyou obviously doesn't do a stellar job of it, but it's still much better than what I'd have expected.
Jooles : Too complicated, too many speech bubbles -- Yes, this is a very chatty manga, as evidenced by the drama, psychological and mystery genre tags. Not all shounen manga have to be brainless action + harem ecchi, though Spiral does have a (plot-mandated) action component.
MarineHaddock : Forced/rushed romantic development; SCKing88, Revelmonk : Not enough romance -- Actually, a strong romantic focus would have been unsuited to the themes and mood of the story. This would probably have got better ratings if Ayumu had conveniently fallen for one of the Blade Children, thus giving him a more "realistic" reason to desire their salvation, but in my opinion that would have been detrimental both to Ayumu's role as a (rather atypical) hero, and to Hiyono's function in the plot and Ayumu's life. (I'm always appreciative of an author who creates love interests who have a reason to exist other than to be the protagonist's prime motivation in everything he does) And the romantic development being postponed to the last volume has several valid reasons, mostly linked to Ayumu's continued sense of inferiority and the resulting inability to break free of his childhood crush prior to events in the latter volumes.
Tl; dr : If you like the sound of "a dramatic psychological mystery shounen with sci-fi elements, a romantic subplot, and tragic undertones," and are not set on the "a truly strong protagonist should just kill everyone who gets in his way" mindset, Spiral - Suiri no Kizuna is well worth a read.