Simon & Garfunkel’s Mrs. Robinson, espically the opening guitar lick, makes a good ringtone.
My generic ringtone is the intro to Wilco’s “Casino Queen”. The ringtone for my home phone # and wife’s cell # is a clip of Fleetwood Mac’s version of “Talk To Me Baby”.
As I was going through the James Bond audiobooks, I tended to change my ringtone according to the book I’m listening to. It shouldn’t be to obvious it’s JB though.
This was a nice one : Thunderball OST - 08 - Death Of Fiona - YouTube
As I’m now having a break in the listening department and the cycling season has begun, I picked this one Rodania.mp4 - YouTube , of course at an unobtrusive volume at work.
I like the theme from “Mission: Impossible.” It starts out very quiet then gets louder and louder.
Since my favorite album of all time is Mike Oldfield’s Tubular Bells 2, I started out with “Sentinel” which starts quiet and gets louder. However I found that it took a long time for me to actually hear it. I switched to “The Bell” which starts with a nice loud chord.
Since that is probably too weird, you can try “Like a Rolling Stone” which starts with a nice crash of the drums.
I used to rock Slayer’s “Raining Blood” for a long time. Then some co-workers pleaded for a change - I really can’t understand why 
Now I settled for a quieter song: Byrds - Wasn’t born to follow. Since I got a ringback service through these fine folks I moved Slayer undercover - joke’s on them!
I currently have the closing theme from Lost in Space Lost in Space - 1967 - Ending Theme Song - TelevisionTunes.com
It’s jazzy and a good dog-whistle for geeks.
My IM tone is the Jetson’s doorbell.
My general ringtone is the chorus to Scissor Sisters - “I Can’t Decide”. But as mentioned earlier, it’s fun to link specific contacts to specific songs. Like, the ringtone for my wife is Gretchen Wilson - “Redneck Woman”. And for my brother-in-law, it’s “The Freaks Come Out At Night”.
I use the super mario bros Star theme for a ring tone and the coin grabbing sound effect for texts. They make me happy on the inside.
Well? Did I win? Where’s my nothing?
I use this 688 power plant casualty alarm. It is also my 5 am wakeup alarm tone. I also use it if I need to wake my husband up for some reason. After 20 years in the sub fleet it gets him upright on spinal reflex <evil grin> It also is his dedicated ringtone, so if I am shopping or on base for any reason, it tends to get peoples attention for some reason 
I recently had the SO download a new ringtone for me. It’s from Blade Runner - the tone Deckerd’s car phone makes when he dials up J F Sebastian’s place and Pris answers. It makes my phone sound all sci fi and stuff.
Mine is Penny saying “Knock, knock Sheldon”…
I use the opening theme from Red Dwarf. Easy to hear and tends to generate a lot of smiles when it rings in public.