Painting speaks to our senses. Of all our feelings, which is the most fundamental? Well, you can safely assume that, when it came to assembling an exhibition called Love, curators were not stumped for pictures. Love surely counts among culture's most ubiquitous themes. And hardly surprising: it is a universal force that whips up pretty much a full range of spin-off emotions. So imagine the potential of a National Gallery show on this subject. Love - or so the songwriters tell us - is a many-splendoured thing.

Well, it certainly would be if this exhibition could draw on the full range of our national collection: on the elegant serenity of Van Eyck's Arnolfini marriage, on Titian's dramatic pageant of a lovestruck Bacchus, on Ruben's billowing image of Delilah's betrayal, on the sensual eroticism of Velázquez's gazing Venus.

But this is a travelling show. And our greatest masterpieces tend either to have very busy diaries or, like revered old ladies, have grown far too frail to be shunted about, and so this latest exhibition must instead explore love in its many and varied forms with just a couple of dozen canvases and a scattering of sculptures drawn often from the less popular parts of the national collection, as well as a handful of regional galleries and private homes.

Love, ranging from the flagrant eroticism of Cranach's sly Venus to Tracey Emin's needlework whine, spans 500 years of art history. Some works are less well-known pieces by the world's greatest masters as in the case of Turner and Goya. A few - as with Vermeer's young woman at her virginal for example, are the best. Thank God that love is not always blind.

Thinkers have been struggling to define love - at once the most simple and most complex of passions, the most instinctive and yet confusing of feelings, since the days of Plato's Symposium when Phaedrus kicked off one of philosophy's more famous arguments by arguing that Eros was the oldest of the gods (because he had no father or mother). And this new show sets out to capture a sense of the multifaceted variety of the subject it tackles. Here is love from the familial to the romantic, from the sexual to the divine. Here is the meditative maternal tenderness of Raphael's Madonna of the Pinks. But here too are the homosexual passions of David Hockney. We Two Boys Together Clinging was painted when he was still a student in 1961. The liaison it celebrates, with all the jubilant frenzy of a piece of public lavatory graffiti, was still against the law.

Here is the pale temptation of Cranach's coy Venus - one of the most enticing works in the show. Her little pink toes toy erotically with a branch as she lures the spectator with a sly cat-like glance, apparently oblivious to her crying companion, a mournful bee-stung Cupid, who cautions that love's honeyed syrups can be stolen only at a cost. But here too is Marc Quinn's 2001 sculpture of an embracing couple, Kiss. The luminous perfection of the Macedonian marble may be what first strikes you. But look again. One of the lovers has a limb missing. Another has something odd about his arm. This image of tender engagement, for which two of the creator's close friends posed, disturbs our expectations and questions our ideals. Artistic love does not always have to belong to the conventionally beautiful.

Love is ... almost anything except a stereotype. The contemporary and the historical come together with enriching effect. What, at first encounter, might seem more radically different from each other than a little china rabbit by Grayson Perry and Guercino's rendition of an Old Testament scene? The two works, as so often in this show, speak to each other. Where Guercino paints Hagar and Ishmael, a slave woman and her famished son in the desert, Grayson writes over and over on his rabbit a fetishistic imprecation: “God please keep my children safe.” Both works evoke the anxieties of parental love.

Often it is the passions of the painters themselves that are captured in painting. Rossetti's Astarte Syriaca stands, luscious and dangerous, at the centre of a painting that burns with the flame of desire. Rossetti was falling in love with his model, Jane Morris, but she was also the wife of his close friend. This picture is a testimony to the feelings of a man whose own famously beautiful wife has recently died and whose re-awakening senses prompt the turmoil and longings that lost love leaves in its wake.

The Russian Marc Chagall, one of art history's greatest hymnodists to love, repainted his Bouquet with Flying Lovers after the death of Bella, his wife. In this final version he depicts himself leaning out of a window, hopelessly clinging to his wraith-like beloved as a sleeper clings to dissolving dreams. The canvas is infused with the yearning and wonder of his feelings. It tells a haunting story in its own right, but, hung alongside the works of Joseph Wright of Derby and Stanley Spencer, it also takes on other meanings. It represents wedded bliss in a line-up in which two other painters, respectively, show young love and the longstanding passions of age. Spencer's shambolic old couple is particularly poignant - not least because the artist himself had just married Patricia Preece, a liaison that would never be consummated. Does he paint this rapt couple out of feelings of longing? Does he capture his own lost dream?

If you were just wandering through a gallery, you would probably pass by Joseph Wright's faintly dull portrait of the newly-wed Coltmans. But in the context of this show, the easiness of their tender intimacy is given a focus that it might otherwise lack. And if you want to meet this couple again go and look at Wright's most famous picture: his dramatic Experiment with a Bird in an Air Pump. There they are again among the faces that crowd to witness a groundbreaking moment - except where all the other onlookers stare at the experiment enthralled, the young lovers still have eyes for each other alone.

A connection between the selected paintings and the rest of the National Gallery's collection is probably the greatest pleasure of this show. An exhibition that might otherwise feel a little thin has incredible back-up. It encourages you to wander off and make your own discoveries.

This show asks us to fall in love with painting. It slips down as easily as an aphrodisiacal oyster.

Love is at the National Gallery (020-7747 2596) from Thursday

The top five works of love

The Kiss (Rodin, 1901)

Rodin may not have considered his rendition of a pair of Dante-esque lovers (above) his finest work, but the blend of realism and idealism have made this sculpture one of the world's most famous images of erotic love

The Venus de Milo

Probably the world's most famous classical image is this armless statue of what was originally believed to be the goddess of love

Amor Vincit Omnia (Caravaggio, 1601)

Love does indeed conquer all in this impudently pornographic painting of a teasing boy Cupid

The Ecstasy of St Theresa (Bernini, 1647-52)

Divine love comes down to Earth in a high-Baroque masterpiece that captures the moment of orgasm in marble

The Kiss (Constantin Brancusi, 1916)

Making a direct reference to Rodin's famous work, a pair of embracing lovers melt back into one block in this piece of iconic modernist carving

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