Susan Hiller, Tate Britain, London

It has taken decades for this American artist to grow out of her wordy cleverness – and the terrifying results have been more than worth the wait

In the week that the art critic Tom Lubbock was buried, endings were everywhere; which made a visit to Susan Hiller's retrospective at Tate Britain apposite, if poignant. I don't know if Tom admired Hiller's work – one of the joys of him was that you never knew what he'd like – but you feel Hiller would have recognised his disappearance, the puzzlement of his readers and friends.

Seeing her show just now, it struck me that Hiller, 70, has always dealt with one, big question: what happens after? When nobody speaks a language any more, is it still a language? When the Jews of Germany are annihilated, are they in any sense still there? Where does the image go when a television is switched off, what happens to a painting if you unravel its canvas? This has been her inquiry for 40 years now, in too many mediums to name: among them film and cloth, installation, drawing, painting; in sound, concept, video, weaving. One of the values of being able to weigh up a life's work, especially work as disparate as Hiller's, is that you can follow its paths, see where it's been going. In Hiller's case, what hits you is how consistent her questioning has been, in terms both of what she asks and, by and large, of how brilliantly she asks it.

If you had only seen a couple of Hiller's pieces from the past 40 years, it would be easy to come away with the wrong idea of her. In the 1980s, she seemed too interested in a literal paranormal, and too busy. Monument (1981) consists of a cross-shaped wall-piece made up of 41 blown-up photographs of memorial tablets to civic heroes. Thus Henry James Bristow, aged eight, who "saved his little sister's life by tearing off her flaming clothes but caught fire himself", and others who exposed themselves to death by diptheria, drowning, scalding by steam or molten sugar, runaway trains, poison gas.

In front of this, Hiller placed a wooden bench with a metal plaque saying 1980-81, Monument, Susan Hiller, so that her work encompasses both its own death and its maker's. On this bench again is an old-fashioned cassette recorder which plays a tape of the artist's voice discussing the afterlife. In bringing together sound and image – the Turner Prize hadn't been invented yet, remember – Monument was groundbreaking. But it was also too much too clever, made up of too many things; a flaw of which Hiller has rid herself since.

Already there in Monument was a sense that artworks and artists die too, that mortality begins at home. Hiller's interest in disappearance is intrinsic rather than academic, applies to her as much as the next man. Her work can be very, very frightening, but you feel that Hiller is scared by it as well. She is at her strongest when she is least wordy, when she confines herself to one medium, a single terror.

An Entertainment is the synchronised, four-channel video of a Punch and Judy show, shot in grainy, saturated close-up. The work, its soundtrack swozzled and bellowing, is almost unwatchably frightening, like a snuff movie by Disney. The question it asks is the classic Freudian one: what remains of the terrors of childhood, what do they become? By contrast, The Last Silent Movie is in black and white and consists of subtitles only. A voice speaks, the subtitles translate: "Long ago, everyone spoke Comanche [...] Now we are going to speak Comanche again. We will speak Comanche forever." It isn't true: only a handful of people now use the language, all of them old. Hiller's film is like the voice of a ghost, speaking a dialect of the dead.

Even when Hiller's interest in The Other is annoying, her work is saved by her formal imagination. Witness is a room filled with small speakers dangling from the ceiling by wires, so that you have a sense of being underground, brushing through the buried roots of trees. Each speaker plays the testimony of a witness to a UFO sighting, retailed in dozens of languages: you can listen to what are presumably the words "little green men" in Portuguese, Latvian, etc. This quest into the paranormal bothers me. To my mind, it detracts from the other areas of the unknown – the various afters, the numerous deaths – that Hiller explores so movingly elsewhere. But Witness is brilliant even so, because she has a fantastic eye for the unseen, an ear for the unheard. The film of her J Street Project, in which the camera rests silently on German street signs that still include the word Juden – Jew – is Hiller at her best. Words fail her, sometimes, as they do us all.

To 15 May (020-7887 8888)

Next Week:

Charles Darwent goes bowling with Cory Arcangel at the Barbican

Art Choice

The Museum of Everything, tucked away in Primrose Hill, London, has extended its Exhibition #3 – you have until Friday to see Sir Peter Blake's creepy collectibles. Bridget Riley's 80th birthday is being marked with a National Gallery retrospective. Works by the doyenne of abstract art hang alongside the old masters that inspired her (to 22 May).