Will they rattle you or make you hum? Journalist Dave Simpson picks his top 10.

1. Into the Heart

The phenomenon of Bono often overshadows U2, the band. For many detractors, the singer is a pontificating rock star with wraparound shades who has been accused of not paying enough taxes.

For the legions of U2 fans around the world, he's the dynamic frontman-humanitarian who campaigns for peace and against poverty, and gave 1980s rock (and beyond) a passionate social conscience. However, U2 are four people, not one, and their collective musical chemistry transformed a band formed at Dublin's Mount Temple Comprehensive School into one of the biggest rock groups ever.

That certainly wasn't on the cards when they signed their Island Records contract in the ladies' loo at the London Lyceum. U2's 1980 debut, Boy, is one of the best of the post-punk era, although the partly instrumental Into the Heart suggests that there's already more to this black clad, dodgy-mulleted foursome than meets the eye. Parts of the album showcases The Edge's already trademark bright, breaking-glass guitar sound, inspired by the Skids and Siouxsie and the Banshees, but here he plays a beautiful, virtuoso solo.

Meanwhile, drummer Larry Mullen Jr and bassist Adam Clayton conjure up an almost pre-post-rock soundscape and Bono Vox – born Paul Hewson – is at his impassioned best. Boy erupts with youthful exuberance, but there's a melancholy undercurrent. The singer's mother's death – when he was just 14 – informs many early U2 songs (notably I Will Follow and Out of Control) and perhaps there's more of that emotional turbulence in Into the Heart's stirring, heartfelt ode to childhood innocence.

2. October

October, U2's archetypal "difficult second album", fared better than Boy – reaching No 11 in the UK in 1981 – but is very much an inferior retread, albeit with a more pronounced religious element to the songs, which led to the British music press to view the three-quarter Christian band as Bible-bashing oddballs. Such growing pains aside, the sublime title track further hints at the many metamorphoses to come. The Edge returns to his teenage instrument, the piano, to deliver an almost classical, reflective piece. Bono's lyrics – "October and the trees are stripped bare" – are a metaphor for how 1960s hope had turned to 1980s cold war-era despair. The sentiments could apply today, although, on a technical detail, trees don't completely lose their autumn leaves until well into November.

3. New Year’s Day

By 1983, U2 were one of the bigger "alternative" bands on the gig circuit: contemporaries of New Order, Echo and the Bunnymen and the Cure. However, 1983's mighty War saw them consciously toughen up and take on a more mainstream rock arena. The album sleeve is particularly significant, featuring Boy's fresh-faced young cover star Peter Rowen, but older and angrier, with a split lip. New Year's Day is the first of their chart-steamrollering rock anthems. The Edge peels off some searing guitar, his piano intro is instantly recognisable and Bono is at his most impassioned. Touring had opened the band's eyes to wider political situations, and its lyrics refer to the internment of Polish Solidarity movement leader Lech Welasa and the lifting of martial law. The song was U2's first UK Top 10 hit and is still a radio favourite, especially every January 1st.

4. Sunday Bloody Sunday

The 1983 live video and album, Live at Red Rocks: Under a Blood Red Sky, captured U2's growing power as a live act and became a handy introduction for anyone who'd bypassed the first two albums. What began as a live video experiment, at Colorado's Red Rocks Ampitheatre, was recorded in such inclement conditions that the show was almost called off. The band played a driving, impassioned set under driving sleet and rain with three giant torches sitting atop the rocks and steam coming out of Bono's mouth as he sang.

The footage of the singer carrying a white flag of peace during Sunday Bloody Sunday has been called some of the most iconic imagery in rock history. Propelled by Mullen's military drumbeat, the song itself nods to the infamous Bloody Sunday massacre but makes a heartfelt call for peace in Northern Ireland, with the simple but effective plea, "How long must we sing this song?"

The song captured the growing public mood that enabled the peace process to grow in Ireland. Where Bono had once sung: "I can't change the world / but I can change the world in me" (in Rejoice, from October), it was around this time he seems to have realised that his increasingly popular rock band could have a significant impact on the planet.

5. Bad

Long before your Coldplays and Elbows, U2 were the go-to combo for making intimate sentiments feel universal. Built around the Edge's shimmering guitar riff, this beautifully slow-building song from 1984's Brian Eno/Daniel Lanois-produced The Unforgettable Fire is a case in point. In the late 1970s and 1980s, Dublin was suddenly awash with cheap heroin from post-revolutionary Iran, and Bad documents Bono's heartache as a very close friend succumbed. "A lot of sweet teenage kids, who just liked to smoke a bit of ganja, were offered this cheap high, something beyond their imagination," he explained in 2006. "I tried to describe what it was to feel that rush, that elation, and the go on to the nod, awful sleep that comes with that drug."

At Live Aid in 1985, Bono became so swept up in the song – at one point disappearing off the stage, returning to dance with a girl from the audience – that an epic Bad took all the time allotted for their third song/grand finale. The band were apparently so furious they almost fired him, but the stadium crowd and billions watching on TV were captivated. Rolling Stone later called it "12 minutes that made the band's career".

6. Pride (In the Name of Love)

This 1984 smash was the track unceremoniously dumped at Live Aid, but otherwise it remains one of the band’s cornerstone anthems. The lyrics address the assassination of Dr Martin Luther King Jr, and apply the ideas of non-violence to the Irish situation.

The chorus (“In the name of love / once more in the name of love”) is as huge as any of them. Bono has admitted to mild embarrassment that the lyrics say “early morning, April 4”, when King was killed in the evening, but the subsequent lines “a shot rings out in a Memphis sky / Free at last / They took your life / They could not take your pride” are as dramatic and powerful as anything in their canon.

7. Where the Streets Have No Name

Released in 1987 at the height of the Thatcher/Reagan era, U2's fifth album, The Joshua Tree, cemented their love-hate relationship with the United States, combining rootsy Americana, blasts at Reaganomics, impassioned acoustic rockers and haunting elegies for the victims of South American death squads. It's not, on the face of it, the most obviously commercial album. However, in With or Without You and I Still Haven't Found What I'm Looking For, they had two copper-bottomed global smashes. After the groundwork of Live Aid, MTV and endless touring, the album gave them a No 1 in every major market and took them to a new level of superstardom.

Named after a tree in the Mojave desert, which represented the band’s idea of desert meeting civilisation, the album has sold almost 30m copies and retains a special place in fans’ hearts and the band’s vast repertoire: they’re touring it again this summer for its 30th anniversary.

“I want to run / I want to hide / I want to tear down the walls that hold me inside,” Bono begins, in the album’s surging opener and third single. The lyrics were prompted by his discovery that in Belfast, someone’s street address reveals their social class and religious denomination – so the only escape is to (a mythical place) where the streets have no name. The song was particularly difficult to record; Eno became so frustrated that he almost destroyed the tapes. However, they finally captured a perfect representation of one of their very best songs. The moment when the juggernaut rhythm crashes in over Eno’s introductory organ hum is particularly sensational.

8. One

After The Joshua Tree had critics gushing about "the greatest band in the world", Rattle and Hum – the 1988 Phil Joanou-directed documentary, or rockumentary if you will – U2 found themselves suddenly facing an unexpected backlash. Critics and some fans turned on the film's perceived self-importance and the Dubliners' most heinous fashion crime: wearing cowboy boots and Stetsons.

Meanwhile, as stadium contemporaries Simple Minds were also realising, change was afoot as the Stone Roses, Happy Mondays and acid house ushered in a sea change in pop culture. Suddenly, U2 were seen as earnest and old hat. "We're going to go away and dream it up again," Bono declared, and the band returned as a markedly different beast, beginning with 1991's Achtung Baby, one of their finest albums. Holing up in Berlin's legendary Hansa Studios – birthplace of Iggy Pop and David Bowie's classic mid-1970s albums – brought experimentation and electronic/industrial grooves, although the album's sublime standout is a sparse, eerily lovely ballad.

Recorded as the Berlin wall came down, One is ostensibly about the difficulties of staying together - in 2005, Bono explained that the song is the story of a gay friend, who was coming out but afraid to tell his Christian father.

9. Discotheque

The 1990s was a decade of transformation for the band as they repeatedly dismantled and rebuilt their sound and image. This song from 1997's Pop did both (and, as a consequence, divides opinions among the fanbase). It's a big, goofy, daft but fun house stomper – their most dance-oriented track from their most dance-oriented album - although ironically features one of the Edge's most raucously rocking riffs. "You know you're chewing bubble gum / You know what it is but you still want some / You just can't get enough of that lovie-dovie stuff," Bono sings, ostensibly about Ecstasy, although he has explained that the song has a deeper meaning, about "love … the counterfeit that you can't find."

In the song’s video, the band send themselves up by donning garb like the Village People: Bono is a motorcycle cop, Mullen a cowboy, Clayton a sailor and the usually straight-faced Edge seems to revel in the role of a waxed-tached, crotch-thrusting, leather-chapped S&M/biker role. Never let it be said that U2 don’t have a sense of humour.

10. Stuck in a Moment You Can’t Get Out Of

With typical chutzpah, Bono fanfared 10th studio album All That You Can't Leave Behind by saying that U2 were "reapplying for the job as best band in the world". After years of changes, their 2000 offering returned to their old staples: guitars and drums, sincerity, humanity, and uncomfortable but universal subjects. This gospel-tinged No 2 hit ("You've got to get yourself together / You've got stuck in a moment / And now you can't get out of it …") derives from a conversation Bono imagined having with close friend Michael Hutchence, before the INXS singer's deathin 1997.

“I think other people who have lost a mate to suicide will all tell you the same thing – just overpowering guilt that you weren’t there for that person,” Bono explained. “And then anger and then annoyance. That song is a row between mates. You’re trying to slap somebody round the face, trying to wake them up out of an idea. In my case it’s a row I didn’t have while he was alive.”From tragedy and frustration came one of U2’s loveliest, most touching songs.

By now, the lives, lifestyles, political involvements, houses and hairstyles of our former Mount Temple pupils have changed beyond recognition, but this is as heartfelt and affecting as anything on their debut.

Guardian Service