I haven't ever heard radiohead or U2 come up in the same conversation. I think U2 has a lot of really good songs, they're expert craftsmen of pop. I like U2. I don't think their music is akin to Radioheads, in my opinion it's apples and oranges.
I actively dislike U2, to be honest. I've tried a few of their albums but none of the modern stuff seems to have the actual power of their older, more political music. It has all been disappointing. It reminds me of Coldplay in that it sounds great but to me it feels like there is nothing underneath it. I'll try and listen to some Radiohead singles today, see what I've heard and haven't. Maybe I always see them mentioned together in threads like this. I don't know. I just know I have a very strong mental link of the two, as if they always appear hand-in-hand. As someone who doesn't listen to either much, I'm probably not surrounded by people who are very into either band. Although I did find out that one of my oldest friend is super-into Rancid recently; I mentioned the band sarcastically and she exclaimed "I love Rancid!" So sometimes people'll surprise ya.
To add / counter nowaypablo on Radiohead, I think the band is really good for me but not necessarily for everyone. Radiohead makes music that clicks with me, the last puzzle piece to complete my mind, so to speak. It makes sense on a deeper level. This is why a lot of fans reeeally want you to listen to it: if you get into it, there's so much fulfillment to get from their songs. I went to Thom Yorke's concert last year and my god it was the most amazing thing I have ever heard. But I'm really sure that it's not for everyone and it took me really long to get into the band - Yorke always seems to balance between repulsive music and really great music. That being said, I recommend these songs, but don't expect to like them immediately. Subterranean Homesick Alien. From their first big rock album, OK Computer. You've probably heard Karma Police or Creep, but I much prefer this song on the album. Reckoner. Long high-pitched Yorke. Quite different from the first song, isn't it? Go To Sleep. More upbeat. I personally love the opening guitars and the changing atmosphere 1:30 in. This is a great example of Thom only just singing good (to someone who isnt a fan), and distortions thrown in that might put ya off. Little by Little - live from the Basement, from 43s on. I always swing with this version. Give Up The Ghost, also live. A song for when I feel weak, when you want to give up. Hope that's a good representation of the band. If there's a particular song you like, I can recommend more of that. Also, pablo, AustinBrock is back online! Whoo!
I'm going to be an obnoxious prick again to plug in my favorite band, if you're going to listen to Radiohead's songs. Note: In Rainbows is the most friendly and summarizing album, you could start there or: if you're into rock and more hesitant of electronic/"Weird shit" listen to: Paranoid Android Karma Police Street Spirit (Fade Out) Creep My Iron Lung These are their biggest rock hits, from albums The Bends and OK Computer. If you can dig deeper into some nonconventional stuff, listen to the Hail to the Thief and Amnesiac albums, especially: 2+2=5, Sit Down Stand Up, Backdrifts, Myxomatosis, and A Wolf at the Door (<-all four grow on you quickly)
Pyramid Song, I Will (these are mellow-er)
I apologize and enjoy! edit: I really like radiohead