I saw a Batman thread like this, so I decided to start a Superman one since associating songs with Superman is a really common occurrence in my mind, since sometimes I just think about Superman too much! Some of these associations are weird or even nearly inexplicable since I just like associating Superman with random things.
Everything You Want by Vertical Horizon - I think of it as being about the Clark Kent and Superman love triangle with Lois Lane, due to the fact that it switches from "he is everything you want" to "I am everything you want" at the end. Most of the rest of the lyrics don't actually make sense with this, granted...
Misunderstanding by Genesis - The vibe of this song just really matches a "Clark Kent pining over Lois" mood to me.
Come Out and Play by The Offspring - OK, this is a weird one. I think of the line "You gotta keep 'em separated" as referring to keeping his civilian and superhero lives separated. Specifically, in the early post-Crisis era when Clark was dating Cat Grant, I remember one occasion when he tried to interfere with Cat's custody issues with her son and it was kind of a mess, and I felt like it was a possibly questionable decision to use his Superman identity to meddle with a situation with his girlfriend. The rest of the lyrics are about youth gang violence, which also fits because in the era there were stories about that same topic. So, yeah.
Kryptonite by Three Doors Down - Err, no surprise here, lol. But to make this more interesting, I'll say that I specifically imagine this to be about Superman/Clark's relationship with Lois Lane, and how in certain a sense she's his real greatest weakness. A lot of the specific lyrics seem to fit this well.
Cool Kids by Echosmith - I imagine Clark singing this about trying to fit in society when he's such a different kind of being, or something like that.
Come As You Are by Nirvana - I misheard "old memoria" as "no memory" and associated with an episode of the Adventures of Superman where there was a drug that made people lose their memory, and the lines about not having a gun with an episode where Clark Kent held his finger against a man's back pretending it was a gun...yeah...wow I really reach to associate songs with Superman.
Complicated by Avril Lavigne - Lois Lane talking to Superman about his secret identity making their romance more complicated than it need be.
Personal Jesus by Depeche Mode - Apparently this song is about a great friend can be like a "personal Jesus" to you, and I think Clark could be that kind of person.
Policy of Truth by Depeche Mode - If Superman were to tell everyone his secret identity, that would certainly cause a lot of problems, wouldn't it?
Enjoy the Silence by Depeche Mode - I don't really think I have a reason why, but I imagine Superman singing this to Lois Lane.
People are People by Depeche Mode (man, when am I going to give this band a break as far as associating them with Superman goes?) - I imagined it being about the idea of Batman and Superman being nemeses rather than friends, especially since the friend interpretation makes a lot more sense in many ways.
Steady As She Goes by The Raconteurs - Uhhhhh...it's hard to say. Maybe it's because certain parts of the lyrics are about settling down and stuff like that but some parts of the song are intense-sounding, which sort of captures the duality of Superman to me?
Dangerous by Big Data - I imagine this being about Superman being hunted down by the government.
Beat It by Michael Jackson - I imagined this song with a fun double meaning - Clark Kent "beats it" when trouble comes his way, and then appears as Superman, causing the criminals to "beat it"! However, me associating this song with Supes is not really something I do anymore, since I'm a big fan of Michael Jackson and thus mostly associate his songs with himself, if that makes sense.
Radioactive by Imagine Dragons - Associated it with the Adventures of Superman episode "Superman in Exile" where Superman becomes radioactive. Silly...
Head Over Feet by Alanis Morissette - Sounds a LOT like Lois' relationship with Clark to me! (Finally one that makes a bit of sense.)
There are probably even more to be honest, but that's a good enough start...hopefully other people will have answers that are less of an extreme stretch than most of mine are...