I trying to get more interested in bass, to maybe one day buy one, but want to be sure its a sound I can accept.

I'm not that sure on gene, but I'm not so much into jazz or funk or that slapping stuff...

Gorillas has a few songs with some nice bass
Blink 182
Rise Against
Pierce The Veil - "King For A Day" ft. Kellin Quinn
Good Charlotte

what are bands/songs are there that have a bass guitar that stands out more?
First bands that come to mind are:
Muse, Tool, Riverside, Ne Obliviscaris, Cynic, and RHCP

Those are all bands whose music regularly involves bass lines that don't 'follow' the guitar

I think Ne Obliviscaris does it the best though:
Guitars & Gear:
Parker Nitefly M
Sumer Metal Driver
Ibanez RGD2120Z
Two Notes Torpedo CAB
Last edited by Emperor's Child at Mar 21, 2015,
The Who comes to mind immediately john entwhistle was a monster bass player. check out Talas. this was billy sheehans original band.
The Who without a doubt. John Entwistle is the king of bass guitar. Geddy Lee of Rush also has some great bass riffs.
The Police

On tour in the US, Sting bought a fretless bass having never played one before and uses it at the concert that very evening. Legend.
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Chris Wolstenholme of Muse does unbelievably well to outperform Matt Bellamy (try Hysteria).
Tim Commerford of Rage Against the Machine (Take the Power Back). Flea of RHCP (just ANYTHING!) and Most funk songs (Good Times by Chic especially)

Marilyn Manson, Nine Inch Nails, Orgy, a lot of three days Grace is on bass too.
now that might not be what you are into at all, looking at the other
suggestions, but theres is a whole music culture based around BASS.
there are actually guys that play Dubstep and likewise stuff on a bass-guitar...
check out Chris Hargreave's Masterclass on YouTube, i wasn't into Dubstep
when i saw it first, but yet it made me think about trying it out!!
You shall check out the albums from Stu Hamm, I like his Outside Of Normal album, very cool... Joe Satriani is playing 2 songs in there
Guitar teacher from Paris - Arranger - Composer - Transcriber
"The Real Me" From The Who, John Entwistle actually outshines Townshend on that one.
Muse for sure! check out Panic Station, Hysteria, and Plug in Baby, but really, since they are a trio, pretty much all their songs have good bass
Honestly check out a lot of trios. Since they usually only have one guitar, the bass is "forced" to play more.
Mr Big- one of my favorite bands- Billy Sheehan is amazing
The Winery Dogs- also with Billy
some Joe Satriani songs actually have some audible bass
The Who
Daft Punk- lots of bass lines. Check out Around the World
Rage Against the Machine, Green Day, RHCP- I dont like these bands but the bass playing is quite active
Aerosmith- Sweet Emotion
Guns n Roses on some songs
Breaking Benjamin- lots of bass surprisingly
Sixx:AM- Nikki Sixx started the band so that obviously has some bass leanings. Check out Live Forever
Damn near every bass player I know has told me they got into bass cause of the Chili Peppers. Geezer Butler from Black Sabbath is my personal favorite. I also love Lemmy, even though a lot of people will say he plays it too much like a guitar player.
Check out Paul on Sgt Peppers, The White Album, and Abbey Road and on the prog rock side, no bassist stands out as much as Chris Squire from Yes. The '72 live album Yessongs is a great place to start...even better is to watch the vid on youtube so you can not only hear but also see what he's doing...
"Music is the only religion that delivers the goods" - Frank Zappa
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Les Claypool and any of his various projects are pretty bass heavy. Some sweet guitar stuff in there too, but a lot of it is driven by the bass.
Well they don't use an actual bass guitar in most of the studio stuff, but seriously check out the doors. Ray does the bass with his keyboard but they seriously have some of the most amazing bass grooves ever. Check out anything of theirs and it will usually just have one of those killer basslines that grabs you, especially shit from their first album, and definitely check out LA woman. I'm all about guitar but if I was ever going to grab a bass it would be to play a million doors songs...