I really only discovered U2 for myself a couple years ago. Yes, I knew who they were and even knew a few songs, but the band was not a band I had actually listened to. I would now consider myself a fan. They aren’t my top band, but I really respect their work.
What’s their best album?
Joshua tree
It’s the album that made me love them…and then be sick of them. I can’t listen to ANY U2 now despite knowing they are a quality band.
Achtung Baby. Only album of theirs I own. Transcends their standard recipe and has a bit of swing in their groove. Has One, their best song.
Which is?
My vote is Joshua Tree.
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He said. One.
Joshua Tree.
Rattle & Hum is pretty good and I even like All That You Can’t Leave Behind.
The top songs in number of plays in my iTunes are;
#4 is Rakim by an obscure band called Dead Can Dance. I’m sure you’ve never heard of it. 
Beautiful Day and Still Haven’t Found What I’m Looking For are the other U2 songs in my top 10.
Achtung Baby. Just a few more compelling cuts than Joshua Tree, its only real competition.
[top 5 here]
Top 3:
I feel like this question requires a defense of the choice to not rank Joshua Tree #1. To me, the opening three songs are too similar; these days it’s rare I want to sit and listen to that solid 15 minutes of Edge delay/reverb stylings. The album has polish, but little spark.
Nah, picking a different album requires no defense. You’re picking what you like, not what others think you should like.
If you’re into Pop (the album), just go for it! 
I totally agree. The only song on the album that had any staying power for me is what most people usually rank as their least favorite; of course I’m talking about Bullet the Blue Sky.
I like their albums before Joshua Tree best because they still had a lot of rawness to their sound; I felt like I could feel and hear their passion loud & clear.
I like Joshua Tree the best but Zooropaand Achtung Baby have some cool tunes. Wild Horses comes to mind, along with “Numb”, “Mysterious Ways”, and “Even Better Than The Real Thing”
Oh yeah, and “One”
I can’t really listen to One anymore after basically living through it with my ex-wife.
Did I ask too much? More than a lot
You gave me nothing, now it’s all I got
We’re one, but we’re not the same
Well, we hurt each other, then we do it again
You say love is a temple, love a higher law
Love is a temple, love the higher law
You ask me to enter, but then you make me crawl
And I can’t be holding on to what you got
When all you got is hurt
The Unforgettable Fire. I like the mood and sounds from that album… especially “Wire”.
Read it too quickly.
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Then there’s the ‘secret’ U2 album. Passengers: Original Soundtracks 1
Basically U2 with Brian Eno.
“Original Soundtracks 1 is a studio album recorded by rock band U2 and Brian Eno under the pseudonym Passengers as a side project. It was produced by Eno and was released on 6 November 1995. The album is a collection of songs written for mostly imaginary films (the exceptions being songs for Ghost in the Shell, Miss Sarajevo, and Beyond the Clouds). Due to Eno’s involvement as a full songwriting partner and the album’s experimental nature, the moniker “Passengers” was chosen to distinguish it from U2’s conventional albums. It was commercially unnoticed by the band’s standards and received generally mixed reviews. Guest musicians on the record included Italian opera singer Luciano Pavarotti (on “Miss Sarajevo”) and producer Howie B, who would co-produce U2’s following album, Pop (1997).”
+1. Joshua Tree was phenomenal. Achtung, Baby and Zooropa also get regular play on my iTunes/ipod.
Bad (Live), 1985, Wide Awake in America version.
If you twist and turn away…
Joshua Tree, followed closely by Achtung Baby for me.
That’s a new one for me. Usually the least favorites are “Exit” and “Trip Through Your Wires.” Maybe even “In God’s Country.” I’ve literally never heard anyone say “Bullet the Blue Sky” is their least favorite, and I grew up in apparently U2 central in high school.