Yar. I be after a list of real catchy songs of any genre. Or just a song that you really like. The reason will become apparent with time. But for now, please list away!
I like songs that are like a story being told that are in like sections without almost any repetes to the song.

A god example is like.. that one, Don't fear the reaper. I mean yeah, they do have a reacuring line, but besides that each new stanaza is like a new part of the story.

I also like the Pinball Wizard by the Who, who makes the pinball players look like elite warriors. Perhaps you can make a song that make out of the way, weird people or places look awesome in a sense.
"Headfirst For Halos" by My Chemical Romance is a fun song. It's like, all slow then really fast.

"Citizen Erased" is probably one of my favourite Muse songs and it is very much considered a favourite by most Muse fans. It's like a story- similar to what Shades has said. It goes through different sections... it's also awesome.

"Shine Acoustic" by Muse reminds me of Ema. >_>
"Screenager" by Muse is also similar. I've only heard the live version though.

"Showbiz" (by Muse >_>) is an awesome song. It's got a lovely build up to the finale of awesome.
"Black out" (by, again, yes) is great. Nice and slow.
"Fillip", "Overdue", "Stockholm Syndrome", "Hysteria" (especially the latter two) are awesome Muse songs. "Bliss" is great too.
"Recess". "Ruled By Secrecy". "Plug in Baby". "Map of your head". "Uno". "Sober". "Sunburn". "The Gallery". "Space Dementia". "Megalomania". "In your world". "Apocolypse Please".

Those rock. Some are fast and awesome, others are slow and awesome. And awesome.

"Last Time I Tried To Rock You(r world?)" by Mindless Self Indulgence. It's like, do do do do do do do do!
"Planet of the apes" by MSI is great, too. As is "Harry Truman", "I hate Jimmy Page", "Kill the Rock", "Capitol P" and many others.

"Prom" by MSI rocks, too. As does "Bullshit", "Shut me up", "1989"- all kinda MSI's style (techno-punk with added drugs) spliced with more mainstream rock (sort of).

"Diabolical" is a great MSI song. It's like, da da da...
"Tornado" is one of my favs. Especially live. It's like being hit in the face by a brick composed out of musical notes. =/ Which is good, I think.

Just go with any MSI song I think. Generally after I listen to too much of it I feel physically violated so I have to lie down, but it's good stuff.

Of Radiohead:
"Climbing Up The Walls" is a really creepy song of theirs.
"Everything in it's right place" is really nice and smooth. It's like Thom is inside your head!
"Exit Music" is really sad... Romeo and juliet'd. Same with "I want none of this"- very upsetting.
"I might be wrong" has a good feel to it, nice flow. Sort of reminds me of something the Beatles would do.
"Like Spinning Plates" is a beautiful song... really weird- the kind of thing you'd hear playing in your head the one minute before the entire universe ends. Like, as if someone is spending their last day on earth. My friend likes the live version (played only with piano and vocals) but I prefer the studio version which has the drums and vocals (and I think some other instruments) played backwards, then reversed for the final song. The vocals were sung *backwards*, then reversed so the lyrics make sense forwards, but it's warped and weird. It's very good.
"Optimistic" is a good Radiohead song. It's got a very solemn sound.
I really like "Subterranean Homesick Alien", which deals with the issue of alien abduction (it affects 1 in every hundred million americans! =( ).
"2 + 2 = 5" is a good song with a nice rhym.
"Scatterbrain" is one of my fav. Radiohead songs with a unique sounding guitar and pretty cool vocals. Sounds like someone walking through a city and it's all kinda going wrong- but always has been.
"Wolf at the door" is a song about a parent's ordeal when his children have been abducted and the abductor is asking for a ransom, I think. It's sad. =(
"True Love Waits" can only be found done live, since it's never been properly recorded, but it's very sad too.
"You" is a slightly obsesssive love song, and I love it.

Rage against the machine:
- "Know your enemy"; awesome, awesome song. Great 'vibe', man. Plus, socialist revolution makes these songs better.
"Mic Check" has a great song- as does many other Rage songs like "Township Rebellion" and "Take the power back".
"Calm Like a Bomb" is totally awesome, dude. It's like, do do DA DA DA (which is great)!
"Wake up" is one of my favourite Rage songs.
"War Within A Breath" sounds better as the end to "The Battle of Los Angeles" (the album it comes included in) but it's good on it's own, too.

_> That's pretty much all I listen to.
I recommend Hysteria and Stockholm Syndrome by Muse though. They're gr8.
"No Rain" - Blind Melon
"So Cold" - Breaking Benjamin
"All Apologies" - Nirvana
"Santeria" - Sublime
"Dirty Harry" - Gorillaz
"DARE" - Gorillaz
"Pretty Fly (For a White Guy)" - Offspring
"Flagpole Sitter" - Harvery Danger
"The Way" - Fastball