There was allot of great stuff going on in the 80's that was either buried in all that synth or the musicians simply played dumb to fit was was needed for radio. Case in point? Terri Bozzio. During his Zappa years he really showed off but in Missing Persons you didn't even know he was there unless you knew music. And look at him now, constant tours and clinics dragging that insane kit of his around. Someone mentioned Duran Duran, another good one. Those guys are all top notch musicians that never really showed off that much, (you'd get little hints here and there). Madonna was always smart and picked only the finest session players, just listen to the True Blue album closely, all those guys are amazing. You know the more I think about it the more I think I would have really enjoyed being a well respected session guy. No, your name wouldn't be in lights, but you'd be an amazing well rounded musician with enough stories from the business to last a lifetime.
As far as songs go hmm...the first grooving bass line that pops in my head from the 80's, The Fixx's Red Skies from their first album
And Stand or Fall
and Golden Earring's Twilight Zone