I used to be only into just rock/punk-rock, but I pretty much like a little bit of everything anymore...
These bands have more than one or two songs that I like:
AFI, Santana, H2O, Bad Religion, Me First & The Gimmie Gimmies, Fuel, Strung Out, Incubus, Trapt, Reel Big Fish, Sublime, RX Bandits, Bubba Sparkxx, Operation Ivy, Pennywise, Lagwagon, DMX, Finch, Pearl Jam, Homegrown, 311, Alkaline Trio, ALL, Beastie Boys, Tenacious D, Boy Sets Fire, Face to Face, Allister, 2 Pac, Weakerthans, X-Ecutioners, Yellowcard, New Found Glory, Dr. Dre, Rancid, Jimi Hendrix, Ataris, Bouncing Souls, Weezer, Spineshank, Voodoo Glow Skulls, Tool, NOFX, Jay Z, Thursday, Beatsteaks, Less Than Jake, Taking Back Sunday, Mighty Mighty Bosstones, Anti-Flag, Swollen Members, Snoop Dogg, Ben Folds, Flogging Molly, Moka Only, N.E.R.D., Bob Marley, No Use For A Name, Midtown, Ramones, Bush, Counting Crows, MXPX, Lynard Skynard, Dashboard Confessional, Bone Thugs and Harmony, Against All Authority, Nirvana, Offspring, Lucky 7, Green Day, Staind, Rage Against The Machine, The Who, Daycare Swindlers, Evanesence, Foo Fighters, Mad Caddies, Millencolin, Red Hot Chili Peppers, Saves The Day, Rufio, Sum41, Slipknot, Vandals, Early November, Fear Factory, A Perfect Circle, Starting Line, Shyne, Black Flag, AC/DC, Misfits, Dave Matthews...
The list goes on and on, I could probably name a hundred more.
There's also many other bands and singers that only had like one song I liked, but I wont even bother.
Basically, if I like it, I listen to it. I ditched the whole "mainstream sucks! you can't be cool if you listen to any mainstream, at all, period, because." That's just stupid. Sure, there's mainstream songs that are garbage and great underground songs, but there's also underground songs that are garbage and great mainstream songs as well.