The United States of McSweeney's, ed Nick Hornby & Eli Horowitz

These are serious, grown-up stories – honest

It's a bit surprising to get hold of a McSweeney's anthology and find it in book form. The American literary magazine has long been as well known for the innovative, pleasingly offbeat method of its publication as it has for the actual words, whether they appear on a page, a deck of cards, a poster or junk mail. Not every issue of the quarterly from which these stories are taken is formally innovative, but very few of them are just ordinary. Turning the pages of a trickless 300-page hardback selection of those stories, it's hard to accept that you aren't about to be met with another virtuoso stunt.

Like it or not, then, there's an implicit statement even in the binding of this beautiful but not unusual edition, an argument that whatever else McSweeney's Quarterly Concern has become known for, Dave Eggers' project is first and foremost a literary one. This is not an unreasonable case to make. Over the past decade, the influence of McSweeney's on American short fiction has been formative, even as the artefacts that contained that fiction have taken on a broader and hazier cultural life of their own. As Nick Hornby puts it in his introduction: "Here's what you missed... because you judged a magazine by its cover, or because the cover was too pretty or too complicated to open."

Of course, the McSweeney's aesthetic has never been confined to design, and the definitive sense of serious play is still visible in spite of the simplicity of black words on white paper. This is not always a good thing. There isn't a story here that isn't a virtuoso performance of one kind or another – hardly surprising, given the regularly exceptional strength of the source – but there are occasions where the playfulness slips into faux-naivety. In a 2004 critique of the McSweeney's cult, the New York literary journal N+1 attacked that sensibility as a "regressive avant-garde", and that still rings uncomfortably true. Dave Eggers and his devotees, the argument went, "returned to the claims of childhood. Transcendence would not figure in their thought. Intellect did not interest them, but kids did. Childhood is still their leitmotif." (It is not a total coincidence that Eggers' latest project is a novelisation of his screenplay for Where the Wild Things Are.)

Thus, in Kevin Brockmeier's "The Ceiling", in which a town is squashed by the descending sky, and Amanda Davis's "Fat Ladies Floated in the Sky Like Balloons", in which you can guess what happens, literalised metaphors serve to reanimate stories that might otherwise feel stale. Elsewhere, as in Wells Tower's "Executors of Important Energies", a deliberately flat language neutralises events that would otherwise be tragic and remakes them as a curiosity.

When these stories don't work, some variation on these problems is often the root. When they do, you quickly forget the provenance or the format of what you are reading. And there are plenty of gems here. Pia Z Ehrhardt's "How it Floods" finds great tenderness in the aftermath of domestic violence and torrential rain; Tom Bissell's "God Lives in St Petersburg", my favourite in the collection, charts the moral decline of an American missionary in a former Soviet republic to a devastating and entirely human conclusion. Something similar is going on in Rajesh Parameswaran's "The Strange Career of Dr Raju Gopalarajan", which follows Gopi, a discombobulated Indian immigrant who masquerades as a doctor and starts treating patients.

There's a kind of a theme here, a thoroughly American one, and it runs throughout the anthology: immigrants and newcomers, untethered by geography or circumstance, and desperate to find new rules by which to live. At its best, the McSweeney's imprimatur has been a catalyst for a stream of superb short fiction that grapples with these questions, and – while it's a shame that such marvellous writers as T Coraghessan Boyle and Michael Chabon have been excluded, presumably because they need no further help to build a reputation – that mission is by and large fulfilled here, too. What problems there are are the result of writing that seems, rather like those troubled newcomers, to pay too much attention to a cultural environment that can sometimes be suffocating.